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Sparse recovery from quadratic measurements with external field Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-23 Augustin Cosse
Motivated by recent results in the statistical physics of spin glasses, we study the recovery of a sparse vector , where denotes the -dimensional unit sphere, , from quadratic measurements of the form where have i.i.d. Gaussian entries. This can be related to a constrained version of the 2-spin Hamiltonian with external field for which it was shown (in the absence of any structural constraint and in
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Robust methods for multiscale coarse approximations of diffusion models in perforated domains Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-16 Miranda Boutilier, Konstantin Brenner, Victorita Dolean
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale numerical methods, this coarse space is spanned by locally discrete harmonic basis functions. Along the subdomain boundaries, the basis functions are piecewise polynomial
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Numerical simulation of nonlinear fractional delay differential equations with Mittag-Leffler kernels Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-12 Zaid Odibat, Dumitru Baleanu
This study is concerned with finding numerical solutions of nonlinear delay differential equations involving extended Mittag-Leffler fractional derivatives of the Caputo-type. The main benefit of the used extension is to address the complexity resulting from the limitations of using fractional derivatives with non-singular Mittag-Leffler kernels. We discussed the existence and uniqueness of solutions
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Numerical analysis of a singularly perturbed 4th order problem with a shift term Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-10 Sebastian Franz, Kleio Liotati
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with a stability result we have estimates for the subsequent numerical analysis. With classical layer adapted meshes we present a numerical method that achieves supercloseness
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Two linear energy-preserving compact finite difference schemes for coupled nonlinear wave equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-10 Baohui Hou, Huan Liu
In this paper, we propose and analyze two highly efficient compact finite difference schemes for coupled nonlinear wave equations containing coupled sine-Gordon equations and coupled Klein-Gordon equations. To construct energy-preserving, high-order accurate and linear numerical methods, we first utilize the scalar auxiliary variable (SAV) approach and introduce three auxiliary functions to rewrite
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Solving the two-dimensional time-dependent Schrödinger equation using the Sinc collocation method and double exponential transformations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-09 S. Elgharbi, M. Essaouini, B. Abouzaid, H. Safouhi
Over the last four decades, Sinc methods have occupied an important place in numerical analysis due to their simplicity and great performance. An incorporation of the Sinc collocation method with double exponential transformation is used to solve the two-dimensional time dependent Schrödinger equation. Numerical comparison between the double exponential and single exponential approaches is made to
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Improved uniform error bounds on an exponential wave integrator method for the nonlinear Schrödinger equation with wave operator and weak nonlinearity Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-05 Jiyong Li, Qianyu Chen
In this paper, we establish the improved uniform error bounds for the Lawson-type exponential wave integrator Fourier pseudo-spectral (LEWIFP) method for the nonlinear Schrödinger equation with wave operator (NLSW) and weak nonlinearity characterized by a small constant . We first convert the NLSW to a coupled system and then consider the LEWIFP method for the coupled system. The LEWIFP method is proved
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On the homogeneous torsion problem for heterogeneous and orthotropic cross-sections: Theoretical and numerical aspects Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-02 Bruno A. Roccia, Carmina Alturria Lanzardo, Fernando D. Mazzone, Cristian G. Gebhardt
For many years, torsion of arbitrary cross-sections has been a subject of numerous investigations from theoretical and numerical points of view. As it is well known, the resulting boundary value problem (BVP) governing such phenomenon happens to be a pure Neumann BVP and, therefore, its solutions are determined up to a constant. Among a large plethora of finite element method (FEM) techniques that
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A perturbed twofold saddle point-based mixed finite element method for the Navier-Stokes equations with variable viscosity Appl. Numer. Math. (IF 2.8) Pub Date : 2024-04-02 Isaac Bermúdez, Claudio I. Correa, Gabriel N. Gatica, Juan P. Silva
This paper proposes and analyzes a mixed variational formulation for the Navier-Stokes equations with variable viscosity that depends nonlinearly on the velocity gradient. Differently from previous works in which augmented terms are added to the formulation, here we employ a technique that had been previously applied to the stationary Boussinesq problem and the Navier-Stokes equations with constant
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Local and semi-local convergence and dynamic analysis of a time-efficient nonlinear technique Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-29 Ioannis K. Argyros, Krzysztof Gdawiec, Sania Qureshi, Amanullah Soomro, Evren Hincal, Samundra Regmi
The examination of nonlinear equations is essential in diverse domains such as science, business, and engineering because of the widespread occurrence of nonlinear phenomena. The primary obstacle in computational science is to create numerical algorithms that are both computationally efficient and possess a high convergence rate. This work tackles these problems by presenting a three-step nonlinear
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A new linearized second-order energy-stable finite element scheme for the nonlinear Benjamin-Bona-Mahony-Burgers equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-29 Lele Wang, Xin Liao, Huaijun Yang
In this paper, a novel linearized second-order energy-stable fully discrete scheme for the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation is introduced, along with a superconvergence analysis of the conforming finite element method (FEM). Through skillful decomposition of the nonlinear term , a new linearized second-order fully discrete scheme is developed. This scheme requires fewer iterations
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Error analysis of a reduced order method for the Allen-Cahn equation⁎ Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-29 Yayu Guo, Mejdi Azaïez, Chuanju Xu
In this paper we carry out an error analysis for a reduced order method for the Allen-Cahn equation. First, an ensemble of snapshots is formed from the numerical solutions at some time instances of the full order model, which is a time-space discretisation of the Allen-Cahn equation. The reduced order model is essentially a new spatial discretisation method by using low dimensional approximations to
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Superconvergence analysis of a two-grid BDF2-FEM for nonlinear dispersive wave equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-28 Conggang Liang, Dongyang Shi, Longfei Guo
The aim of this paper is to study the superconvergent behavior of a two-grid finite element method (FEM) with 2-step backward differential formula (BDF2) for nonlinear dispersive wave equation. By introducing an auxiliary variable for the original variable , the problem is transformed into a parabolic system. With the help of the combination technique of the interpolation and Ritz projection, the superclose
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A matching Schur complement preconditioning technique for inverse source problems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-26 Xuelei Lin, Michael K. Ng
Numerical discretization of a regularized inverse source problem leads to a non-symmetric saddle point linear system. Interestingly, the Schur complement of the non-symmetric saddle point system is Hermitian positive definite (HPD). Then, we propose a preconditioner matching the Schur complement (MSC). Theoretically, we show that the preconditioned conjugate gradient (PCG) method for a linear system
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An innovative Fibonacci wavelet collocation method for the numerical approximation of Emden-Fowler equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-25 Manohara G, Kumbinarasaiah S
This article presents a novel approach using the Fibonacci wavelet collocation method (FWCM) for the numerical solution of Emden-Fowler-type equations. The Emden-Fowler equations are a class of nonlinear differential equations that arise in various fields of science and engineering, particularly in astrophysics and fluid dynamics. Due to their nonlinear and singular nature, the conventional approaches
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Computing compact finite difference formulas under radial basis functions with enhanced applicability Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-21 Yanlai Song, Mahdiar Barfeie, Fazlollah Soleymani
In this work, we use the combination of radial basis functions (RBFs) and polynomials to derive compact finite difference (FD) formulas. We use RBFs and integrated RBFs (IRBFs), to obtain two sets of formulas: RBF-Hermite FD (RBF-HFD) and IRBF weight formulas. The analytical coefficients and truncation errors for these formulations are computed for the first derivative, second derivative, and 2D Laplacian
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A Crank-Nicolson WG-FEM for unsteady 2D convection-diffusion equation with nonlinear reaction term on layer adapted mesh Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-21 N. Kumar, S. Toprakseven, N. Singh Yadav, J.Y. Yuan
This paper is contributed to explore how a Crank-Nicolson weak Galerkin finite element method (WG-FEM) addresses the singularly perturbed unsteady convection-diffusion equation with a nonlinear reaction term in 2D. The problem and some asymptotic behavior results are given for the exact solution and its derivatives with the parameter . These results are essential for proving the uniform convergence
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Numerical properties of solutions of LASSO regression Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-20 Mayur V. Lakshmi, Joab R. Winkler
The determination of a concise model of a linear system when there are fewer samples than predictors requires the solution of the equation , where and , such that the selected solution from the infinite number of solutions is sparse, that is, many of its components are zero. This leads to the minimisation with respect to of , where is the regularisation parameter. This problem, which is called LASSO
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Legendre expansions of products of functions with applications to nonlinear partial differential equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-20 Rabia Djellouli, David Klein, Matthew Levy
Given the Fourier–Legendre expansions of and , and mild conditions on and , we derive the Fourier–Legendre expansion of their product in terms of their corresponding Fourier–Legendre coefficients. We establish upper bounds on rates of convergence. We then employ these expansions to solve semi-analytically a class of nonlinear PDEs with a polynomial nonlinearity of degree 2. The obtained numerical results
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Parallel cloud solution of large algebraic multivalued systems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-16 M.A. Rahhali, T. Garcia, P. Spiteri
The present paper deals with the resolution on cloud architecture of synchronous and asynchronous iterative parallel algorithms of stationary or evolution variational inequations formulated by a multivalued model. The performances of synchronous and asynchronous iterative parallel methods are compared with previous ones obtained on cluster or when grid architecture is used. Thanks to the properties
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A spectral iterative algorithm for solving constrained optimal control problems with nonquadratic functional Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 Z. Nikooeinejad, M. Heydari
The numerical approximation of the solution to Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) in constrained optimal control problems (COCPs) with nonquadratic functional is studied in this investigation. Discretizing both of the space and time of HJB PDE by the Legendre collocation method, a nonlinear system of algebraic equations is obtained to find the expansion coefficients
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Efficient spectral and spectral element methods for Sobolev equation with diagonalization technique Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 Xuhong Yu, Mengyao Wang
In this paper, we first introduce a new series of Legendre basis functions by using the matrix decomposition technique, which are simultaneously orthogonal in both - and -inner products. Then, we construct efficient space-time spectral method for linear Sobolev equation using spectral approximation in space and multi-domain collocation approximation in time, which can be implemented in a synchronous
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Extragradient algorithms for solving equilibrium problems on Hadamard manifolds Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 Bing Tan, Xiaolong Qin, Jen-Chih Yao
In this paper, we introduce three adaptive extragradient-based algorithms for solving equilibrium problems in Hadamard manifolds. The proposed algorithms can work adaptively without requiring the prior information about the Lipschitz constants of the bifunctions involved. Moreover, the iterative sequences generated by the suggested algorithms converge to the solutions of the equilibrium problems when
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On iterative methods based on Sherman-Morrison-Woodbury splitting Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 Dimitrios Mitsotakis
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems and especially for systems involving matrices that are perturbations of circulant or block circulant matrices. Such matrices typically arise in the discretization of differential equations using finite element or finite
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WENO scheme on characteristics for the equilibrium dispersive model of chromatography with generalized Langmuir isotherms Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 R. Donat, M.C. Martí, P. Mulet
Column chromatography is a laboratory and industrial technique used to separate different substances mixed in a solution. Mathematically, it can be modeled using non-linear partial differential equations whose main ingredients are the , which are non-linear functions modeling the affinity between the different substances in the solution and the solid stationary phase filling the column. The goal of
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Numerical analysis of finite element method for a stochastic active fluids model Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 Haozheng Li, Bo Wang, Guang-an Zou
In this paper, we first investigate the well-posedness and regularity of mild solution to a stochastic active fluids model driven by the additive noise. A fully-discrete scheme is proposed for solving the given model, which is based on the finite element method for spatial discretization and the backward Euler method for temporal discretization. By overcoming the difficulty of error analysis caused
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RA-HOOI: Rank-adaptive higher-order orthogonal iteration for the fixed-accuracy low multilinear-rank approximation of tensors Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-15 Chuanfu Xiao, Chao Yang
In this paper, we propose a novel rank-adaptive higher-order orthogonal iteration (RA-HOOI) algorithm to solve the fixed-accuracy low multilinear-rank approximation of tensors. On the one hand, RA-HOOI relies on a greedy strategy to expand the subspace, which avoids computing the full SVD of the matricization of the input tensor. On the other hand, the new rank-adaptive strategy introduced in the RA-HOOI
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A new fast algorithm for computing the mock-Chebyshev nodes Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-09 B. Ali Ibrahimoglu
Interpolation by polynomials on equispaced points is not always convergent due to the Runge phenomenon, and also, the interpolation process is exponentially ill-conditioned. By taking advantage of the optimality of the interpolation processes on the Chebyshev-Lobatto nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev nodes for polynomial interpolation. Mock-Chebyshev
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Computation of pairs of related Gauss-type quadrature rules Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-09 H. Alqahtani, C.F. Borges, D.Lj. Djukić, R.M. Mutavdžić Djukić, L. Reichel, M.M. Spalević
The evaluation of Gauss-type quadrature rules is an important topic in scientific computing. To determine estimates or bounds for the quadrature error of a Gauss rule often another related quadrature rule is evaluated, such as an associated Gauss-Radau or Gauss-Lobatto rule, an anti-Gauss rule, an averaged rule, an optimal averaged rule, or a Gauss-Kronrod rule when the latter exists. We discuss how
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Highly efficient, robust and unconditionally energy stable second order schemes for approximating the Cahn-Hilliard-Brinkman system Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-08 Peng Jiang, Hongen Jia, Liang Liu, Chenhui Zhang, Danxia Wang
In this paper, we present an efficient, robust, and unconditionally energy stable second-order scheme for solving the Cahn-Hilliard-Brinkman (CHB) model, which mathematically describes multiphase flow in porous media. Solving the CHB model is significantly challenging due to its high coupling and nonlinearity. Here, we utilize the scalar auxiliary variable (SAV) method to handle the nonlinear term
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Implicitly linear Jacobi spectral-collocation methods for two-dimensional weakly singular Volterra-Hammerstein integral equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-06 Qiumei Huang, Huiting Yang
Weakly singular Volterra integral equations of the second kind typically have nonsmooth solutions near the initial point of the interval of integration, which seriously affects the accuracy of spectral methods. We present Jacobi spectral-collocation method to solve two-dimensional weakly singular Volterra-Hammerstein integral equations based on smoothing transformation and implicitly linear method
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Spectral-Galerkin method for second kind VIEs with highly oscillatory kernels of the stationary point Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-01 Haotao Cai
In this paper, we discuss an efficient spectral approach for solving a class of second kind VIEs with highly oscillatory kernels possessing the stationary point. First, we use one variable transform to convert the highly oscillatory problem into the long-time one, and then split the long-time problem into a linear system of integral equations by using a dilation approach. Next on each interval we study
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Regularization with two differential operators and its application to inverse problems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-01 Shuang Yu, Hongqi Yang
We introduce a regularization method with two differential operators for solving a linear ill-posed operator equation system. The existence and uniqueness of regularized solutions to the problem are derived. With an a priori as well as an a posteriori parameter choice strategy, convergence and convergence rates of the regularized solution are also obtained. As an application, we apply the regularization
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Numerical discretization for Fisher-Kolmogorov problem with nonlocal diffusion based on mixed Galerkin BDF2 scheme Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-01 J. Manimaran, L. Shangerganesh, M.A. Zaky, A. Akgül, A.S. Hendy
Nonlocal problems involving fourth-order terms pose several difficulties such as numerical discretization and its related convergences analysis. In this paper, the well-posedness of the extended Fisher-Kolmogorov equation with nonlocal diffusion is first analyzed using the Faedo-Galerkin technique and the classical compactness arguments. Moreover, we adopt a BDF2 scheme for time discretization and
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Stability and convergence of BDF2-ADI schemes with variable step sizes for parabolic equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-29 Xuan Zhao, Haifeng Zhang, Ren-jun Qi
In this paper we propose and analyze the alternating direction implicit (ADI) difference schemes in conjunction with the second order backward differentiation formula (BDF2) method with variable time step sizes for solving the two-dimensional parabolic equation. The spatial compact operators are also applied to construct high order ADI scheme. By using the discrete energy method and the positive definiteness
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A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-28 A.F. Hegarty, E. O'Riordan
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used as test functions in one coordinate direction and are combined with bilinear trial functions defined on a Shishkin mesh. The resulting numerical method is shown
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Optimal spectral Galerkin approximation for time and space fractional reaction-diffusion equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-27 A.S. Hendy, L. Qiao, A. Aldraiweesh, M.A. Zaky
A one-dimensional space-time fractional reaction-diffusion problem is considered. We present a complete theory for the solution of the time-space fractional reaction-diffusion model, including existence and uniqueness in the case of using the spectral representation of the fractional Laplacian operator. An optimal error estimate is presented for the Galerkin spectral approximation of the problem under
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Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-22 Xinwu Liu, Ting Sun
To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the plus data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the fidelity is adopted to suppress Gaussian noise, while the -norm is more suitable for detecting and removing impulse
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An explicit substructuring method for overlapping domain decomposition based on stochastic calculus Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-21 Jorge Morón-Vidal, Francisco Bernal, Atsushi Suzuki
In a recent paper , a hybrid supercomputing algorithm for elliptic equations has been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques, such as the Schur complement method for the skeleton
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Finite element analysis of extended Fisher-Kolmogorov equation with Neumann boundary conditions Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Ghufran A. Al-Musawi, Akil J. Harfash
This paper delves into the numerical analysis of the extended Fisher-Kolmogorov (EFK) equation within open bounded convex domains , where . Two distinct finite element schemes are introduced, namely the semi-discrete and fully-discrete finite element approximations. The existence and uniqueness of solutions are established for both the semi-discrete and fully-discrete finite element approximations
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Adaptive H-matrix computations in linear elasticity Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Maximilian Bauer, Mario Bebendorf
This article deals with the efficient numerical treatment of the Lamé equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM). Using BEM, one is faced with the solution of a system of equations with a fully populated system matrix, which is in general very costly. In order to overcome this difficulty
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Monte Carlo method for the Cauchy problem of fractional diffusion equation concerning fractional Laplacian Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Caiyu Jiao, Changpin Li
In this paper, we study a Cauchy problem of fractional diffusion equation concerning fractional Laplacian. We prove the existence and uniqueness of solution to the problem under investigation in Hölder space. Then we apply the Monte Carlo method to solving this Cauchy problem. For the problem with free force term, we derive an unbiased scheme which only produces the statistic error. For the problem
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A discrete-ordinate weak Galerkin method for radiative transfer equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Maneesh Kumar Singh
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting semi-discrete hyperbolic system is approximated using the weak Galerkin method. The stability result for the proposed numerical method is devised. A error analysis is
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Difference potentials method for the nonlinear convection-diffusion equation with interfaces Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-14 Mahboubeh Tavakoli Tameh, Fatemeh Shakeri
In this paper, the difference potentials method-based ADI finite difference scheme is proposed for numerical solutions of two-dimensional nonlinear convection–diffusion interface problems. We employ the Adams–Bashforth method to discretize nonlinear convection terms and the Crank-Nicolson method to discretize diffusion terms. Also, we use radial basis functions (RBF) to approximate the Cauchy data
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Efficient numerical methods for semilinear one dimensional parabolic singularly perturbed convection-diffusion systems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-13 C. Clavero, J.C. Jorge
In this work we deal with the numerical solution of one dimensional semilinear parabolic singularly perturbed systems of convection-diffusion type. We assume that the coupling in the convection terms is weak and also that the coupling reaction terms are nonlinear. In the case of considering different small diffusion parameters at each equation with different orders of magnitude, the exact solution
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Fast multi-level iteration schemes with compression technique for eigen-problems of compact integral operators Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-12 Guangqing Long, Huanfeng Yang, Dongsheng Cheng
In this paper, we present multi-level iteration schemes to solve the eigen-problems of compact integral operators based on the multiscale Galerkin methods. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique results in a fast algorithm. To further minimize computational complexity, we establish Jacobi, Gauss-Seidel and L-H iteration schemes for
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A penalty-type method for solving inverse optimal value problem in second-order conic programming Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-09 Yue Lu, Zheng-Peng Dong, Zhi-Qiang Hu, Hong-Min Ma, Dong-Yang Xue
This paper aims to consider a type of inverse optimal value problem in second-order conic programming, in which the parameter in its objective function needs to be adjusted under a given class that makes the corresponding optimal objective value closest to a target value. This inverse problem can be reformulated as a minimization problem with some second-order cone complementarity constraints. To tackle
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Numerical methods in modeling with supersaturated designs Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-09 N. Koukoudakis, C. Koukouvinos, A. Lappa, M. Mitrouli, A. Psitou
The present study aims to investigate the application of several numerical methods in least square problems, when the design matrix is a supersaturated design. This kind of statistical modeling appears frequently in a majority of applications and experiments where the main scope concerns the identification of the appropriate active factors and possible interactions as well. Several real data sets are
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An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-08 Ali Ugur Sazaklioglu
The main aims of this paper are to investigate the existence and uniqueness results for the solution of an inverse source problem for a multidimensional, semilinear, backward parabolic equation, subject to Dirichlet boundary conditions, and to propose an iterative difference scheme for the numerical solution of the problem. The unique solvability of the difference scheme is established, as well. In
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An asymptotic preserving and energy stable scheme for the Euler-Poisson system in the quasineutral limit Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-30 K.R. Arun, Rahuldev Ghorai, Mainak Kar
An asymptotic preserving (AP) and energy stable scheme for the Euler-Poisson (EP) system under the quasineutral scaling is designed and analysed. Appropriate stabilisation terms are introduced in the convective fluxes of mass and momenta, and the gradient of the electrostatic potential which lead to the dissipation of mechanical energy and consequently the entropy stability of solutions. The time discretisation
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Anderson acceleration. Convergence analysis and applications to equilibrium chemistry Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-02 Rawaa Awada, Jérôme Carrayrou, Carole Rosier
In this paper, we study theoretically and numerically the Anderson acceleration method. First, we extend the convergence results of Anderson's method for a small depth to general nonlinear cases. More precisely, we prove that the Type-I and Type-II Anderson(1) are locally q-linearly convergent if the fixed point map is a contraction with a Lipschitz constant small enough. We then illustrate the effectiveness
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An explicit Fourier-Klibanov method for an age-dependent tumor growth model of Gompertz type Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-02 Nguyen Thi Yen Ngoc, Vo Anh Khoa
This paper proposes an explicit Fourier-Klibanov method as a new approximation technique for an age-dependent population PDE of Gompertz type in modeling the evolution of tumor density in a brain tissue. Through suitable nonlinear and linear transformations, the Gompertz model of interest is transformed into an auxiliary third-order nonlinear PDE. Then, a coupled transport-like PDE system is obtained
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On the growth factor of Hadamard matrices of order 20 Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Emmanouil Lardas, Marilena Mitrouli
The aim of this work is to provide a complete list of all the possible values that the first six pivots of an Hadamard matrix of order 20 can take. This is accomplished by determining the possible values of certain minors of such matrices, in combination with the fact that the pivots can be computed in terms of these minors. We extend known results, by giving a different proof for the complete list
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A new class of symplectic methods for stochastic Hamiltonian systems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Cristina Anton
We propose a systematic approach to construct a new family of stochastic symplectic schemes for the strong approximation of the solution of stochastic Hamiltonian systems. Our approach is based both on B-series and generating functions. The proposed schemes are a generalization of the implicit midpoint rule, they require derivatives of the Hamiltonian functions of at most order two, and are constructed
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Iterative method for constrained systems of conjugate transpose matrix equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Akbar Shirilord, Mehdi Dehghan
This study presents some new iterative algorithms based on the gradient method to solve general constrained systems of conjugate transpose matrix equations for both real and complex matrices. In addition, we analyze the convergence properties of these methods and provide numerical techniques to determine the solutions. The effectiveness of the proposed iterative methods is demonstrated through various
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Krylov subspace methods for large multidimensional eigenvalue computation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Anas El Hachimi, Khalide Jbilou, Ahmed Ratnani
In this paper, we describe some Krylov subspace methods for computing eigentubes and eigenvectors (eigenslices) for large and sparse third-order tensors. This work provides projection methods for computing some of the largest (or smallest) eigentubes and eigenslices using the t-product. In particular, we use the tensor Arnoldi's approach for the non-hermitian case and the tensor Lanczos's approach
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A positivity-preserving well-balanced wet-dry front reconstruction for shallow water equations on rectangular grids Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 Xue Wang, Guoxian Chen
In this paper, a positivity-preserving, well-balanced finite volume scheme on a rectangular mesh is designed based on wet-dry front reconstruction to solve the shallow water equations with non-flat bottom topography. The crucial step is a special piecewise linear representation of the bottom. The flat bottom approximation simplifies the reconstruction of the wet-dry front, which becomes a straight
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Efficient Estimates for Matrix-Inverse Quadratic Forms Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 Emmanouil Bizas, Marilena Mitrouli, Ondřej Turek
In this paper we present two approaches for estimating matrix-inverse quadratic forms xTA−1x, where A is a symmetric positive definite matrix of order n, and x∈Rn. Using the first, analytic approach, we establish two families of estimates which are convenient for matrices with small condition number. Based on the second, heuristic approach, we derive two families of estimates which are suitable for
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A rank-updating technique for the Kronecker canonical form of singular pencils Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 Dimitrios Christou, Marilena Mitrouli, Dimitrios Triantafyllou
For a linear time-invariant system x˙(t)=Ax(t)+Bu(t), the Kronecker canonical form (KCF) of the matrix pencil (sI−A|B) provides the controllability indices, also called column minimal indices, of the system and their sum corresponds to the dimension of the controllable subspace. In this paper we introduce a fast numerical algorithm for computing the sets of column/row minimal indices of a singular
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A space-time Petrov-Galerkin method for the two-dimensional regularized long-wave equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-22 Zhihui Zhao, Hong Li, Wei Gao
In this work, a space-time Petrov-Galerkin (STPG) method is used to numerically analyze the two-dimensional regularized long-wave (RLW) equation. The STPG method is a nonstandard finite element method, that is, both of the spatial and temporal variables of this method are discretized by finite element method. Therefore, it can display the superiority of the finite element method in both spatial and