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Numerical integrator for highly oscillatory differential equations based on the Neumann series Numer. Algor. (IF 2.1) Pub Date : 2024-04-25 Rafał Perczyński, Grzegorz Madejski
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A two-step Broyden-like method for nonlinear equations Numer. Algor. (IF 2.1) Pub Date : 2024-04-25 Jingyong Tang, Jinchuan Zhou
In this paper, based on a nonmonotone derivative-free line search, we propose a two-step Broyden-like method (denoted by TS-BLM) for solving the nonlinear equations. TS-BLM computes one quasi-Newton step at the beginning iterations. When the iterations are close to the solution set of the nonlinear equations, an additional approximate quasi-Newton step is calculated by solving a linear system formed
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Optimal error estimates of penalty difference finite element method for the 3D steady Navier-Stokes equations Numer. Algor. (IF 2.1) Pub Date : 2024-04-23 Xinlong Feng, Xiaoli Lu, Yinnian He
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A dual symmetric Gauss-Seidel technique-based proximal ADMM for robust fused lasso estimation Numer. Algor. (IF 2.1) Pub Date : 2024-04-23 Zheng-Fen Jin, Yibao Fan, Youlin Shang, Weiwei Ding
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Stability improvements for fast matrix multiplication Numer. Algor. (IF 2.1) Pub Date : 2024-04-20 Charlotte Vermeylen, Marc Van Barel
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Smaller stencil preconditioners for linear systems in RBF-FD discretizations Numer. Algor. (IF 2.1) Pub Date : 2024-04-20 Michael Koch, Sabine Le Borne, Willi Leinen
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A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition Numer. Algor. (IF 2.1) Pub Date : 2024-04-18 Zhenhao Lu, Wenping Fan
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Preconditioned golden ratio primal-dual algorithm with linesearch Numer. Algor. (IF 2.1) Pub Date : 2024-04-16 Shan Ma, Si Li, Feng Ma
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An algorithm for approximating implicit functions by polynomials without using higher order differentiability information Numer. Algor. (IF 2.1) Pub Date : 2024-04-16 Kyung Soo Rim
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A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions Numer. Algor. (IF 2.1) Pub Date : 2024-04-15 Xiangtuan Xiong, Jingjing Han
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A class of accelerated GADMM-based method for multi-block nonconvex optimization problems Numer. Algor. (IF 2.1) Pub Date : 2024-04-13 Kunyu Zhang, Hu Shao, Ting Wu, Xiaoquan Wang
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The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids Numer. Algor. (IF 2.1) Pub Date : 2024-04-11 Ali Abdi, Seyyed Ahmad Hosseini, Helmut Podhaisky
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Analytical and numerical studies of the modified Kawahara equation with dual-power law nonlinearities Numer. Algor. (IF 2.1) Pub Date : 2024-04-11 Xiaofeng Wang
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A posteriori error bounds for the block-Lanczos method for matrix function approximation Numer. Algor. (IF 2.1) Pub Date : 2024-04-09 Qichen Xu, Tyler Chen
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Computing parametrised large intersection sets of 1D invariant manifolds: a tool for blender detection Numer. Algor. (IF 2.1) Pub Date : 2024-04-09 Dana C’Julio, Bernd Krauskopf, Hinke M. Osinga
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An Arrow-Hurwicz iterative method based on charge-conservation for the stationary inductionless magnetohydrodynamic system Numer. Algor. (IF 2.1) Pub Date : 2024-04-04 Yande Xia, Yun-Bo Yang
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A family of linearly weighted- $$\theta $$ compact ADI schemes for sine-Gordon equations in high dimensions Numer. Algor. (IF 2.1) Pub Date : 2024-04-04 Qifeng Zhang, Dongfang Li, Wanying Mao
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Extrapolation methods for multilinear PageRank Numer. Algor. (IF 2.1) Pub Date : 2024-04-03 Abdeslem Hafid Bentbib, Maryam Boubekraoui, Khalide Jbilou
Multilinear PageRank is a variant of the PageRank algorithm that takes into account multiple relationships among nodes in a network. This algorithm can make web page ranking more efficient and accurate by considering multiple types of connections at once. The higher-order power method is commonly used to calculate the multilinear PageRank vector due to its ease of implementation and low storage needs
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Stabilization of parareal algorithms for long-time computation of a class of highly oscillatory Hamiltonian flows using data Numer. Algor. (IF 2.1) Pub Date : 2024-04-03 Rui Fang, Richard Tsai
Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long-time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm developed by Lions et al. in 2001, for multiscale Hamiltonian systems. The first method involves constructing a correction operator to improve a given inaccurate coarse
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The second-order modified upwind PPM characteristic difference method and analysis for solving convection-diffusion equations Numer. Algor. (IF 2.1) Pub Date : 2024-04-01 Huimin Ren, Qi Zhang, Zhongguo Zhou
In this paper, the conservation characteristic difference method based on the second-order modified upwind scheme is analyzed for solving the two-dimensional convection-diffusion equations by combining the splitting technique. Along each directional, the intermediate numerical solutions are first computed by the piecewise parabolic method (PPM), where the endpoint values over each domain are solved
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A numerical approach for investigating multiple eigenpairs of a quasilinear elliptic system Numer. Algor. (IF 2.1) Pub Date : 2024-04-01
Abstract The aim of this study is to provide a rigorous description of a numerical approach based on the local min-orthogonal method for finding multiple eigenpairs of a quasilinear elliptic system. By a Rayleigh quotient formulation, the eigenvalue problem is transformed into a constrained variational problem. In this constrained problem setup, we define a novel local L- \(\perp \) selection mapping
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Novel numerical methods based on graded, adaptive and uniform meshes for a time-fractional advection-diffusion equation subjected to weakly singular solution Numer. Algor. (IF 2.1) Pub Date : 2024-03-28 Pradip Roul, S. Sundar
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Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations Numer. Algor. (IF 2.1) Pub Date : 2024-03-28 M. Ben-Artzi, Y. Eidelman, D. Fishelov
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A new approach to the Korpelevich method for solving pseudomonotone equilibrium problems Numer. Algor. (IF 2.1) Pub Date : 2024-03-26 Duong Viet Thong, Xiao-Huan Li, Simeon Reich, Qiao-Li Dong, Dang Huy Ngan
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A generalized fuzzy barycentric Lagrange interpolation method for solving two-dimensional fuzzy fractional Volterra integral equations Numer. Algor. (IF 2.1) Pub Date : 2024-03-26 Ting Deng, Jin Huang, Yifei Wang, Hu Li
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An efficient algorithm to solve the geometric Asian power option price PDE under the stochastic volatility model Numer. Algor. (IF 2.1) Pub Date : 2024-03-23 Abdulaziz Alsenafi, Fares Alazemi, Javad Alavi
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Residual-based a posteriori error analysis of an ultra-weak discontinuous Galerkin method for nonlinear second-order initial-value problems Numer. Algor. (IF 2.1) Pub Date : 2024-03-22 Mahboub Baccouch
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Numerical algorithms for the fast and reliable solution of periodic tridiagonal Toeplitz linear systems Numer. Algor. (IF 2.1) Pub Date : 2024-03-21 Ji-Teng Jia, Yi-Fan Wang
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A spectral approach using fractional Jaiswal functions to solve the mixed time-fractional Black-Scholes European option pricing model with error analysis Numer. Algor. (IF 2.1) Pub Date : 2024-03-20 Fares Alazemi, Abdulaziz Alsenafi, Alireza Najafi
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Multi-block relaxed-dual linear inertial ADMM algorithm for nonconvex and nonsmooth problems with nonseparable structures Numer. Algor. (IF 2.1) Pub Date : 2024-03-20 Yazheng Dang, Liyuan Chen, Yan Gao
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A rotated shift-splitting method for complex symmetric linear systems Numer. Algor. (IF 2.1) Pub Date : 2024-03-18 Snigdhashree Nayak, Debasisha Mishra, Nachiketa Mishra
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Properties and practicability of convergence-guaranteed optimization methods derived from weak discrete gradients Numer. Algor. (IF 2.1) Pub Date : 2024-03-14 Kansei Ushiyama, Shun Sato, Takayasu Matsuo
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Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach Numer. Algor. (IF 2.1) Pub Date : 2024-03-13 Shun Sato
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$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming Numer. Algor. (IF 2.1) Pub Date : 2024-03-11 Tao Zhang, Yong Xia, Shiru Li
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High-order nonstandard finite difference methods preserving dynamical properties of one-dimensional dynamical systems Numer. Algor. (IF 2.1) Pub Date : 2024-03-08 Manh Tuan Hoang
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An $$\alpha $$ -robust analysis of finite element method for space-time fractional diffusion equation Numer. Algor. (IF 2.1) Pub Date : 2024-03-06 Yi Yang, Jin Huang, Hu Li
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On the convergence of the numerical blow-up time for a rescaling algorithm Numer. Algor. (IF 2.1) Pub Date : 2024-03-06
Abstract Berger and Kohn (Comm. Pure Appl. Math. 41, 841–863 1988) proposed an algorithm to compute approximate blow-up times for those evolution equations whose solutions blow up in a finite time and possess a scaling invariance property. Later, Anada et. al (Japan J. Indust. Appl. Math. 35, 33–47 2018) used this algorithm to compute the blow-up rates of various blow-up problems which turned out to
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Inertial self-adaptive algorithms for solving non-smooth convex optimization problems Numer. Algor. (IF 2.1) Pub Date : 2024-03-04 Xin Chen, Peichao Duan
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Jacobian-free explicit multiderivative general linear methods for hyperbolic conservation laws Numer. Algor. (IF 2.1) Pub Date : 2024-03-02 Afsaneh Moradi, Jeremy Chouchoulis, Raffaele D’Ambrosio, Jochen Schütz
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HODLR3D: hierarchical matrices for N-body problems in three dimensions Numer. Algor. (IF 2.1) Pub Date : 2024-03-02 Kandappan V. A, Vaishnavi Gujjula, Sivaram Ambikasaran
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A Lagrange interpolation with preprocessing to nearly eliminate oscillations Numer. Algor. (IF 2.1) Pub Date : 2024-03-01 Bernardo de la Calle Ysern, Pedro Galán del Sastre
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An explicit 16-stage Runge–Kutta method of order 10 discovered by numerical search Numer. Algor. (IF 2.1) Pub Date : 2024-03-01 David Kai Zhang
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High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach Numer. Algor. (IF 2.1) Pub Date : 2024-02-29
Abstract This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance
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Differential equation software for the computation of error-controlled continuous approximate solutions Numer. Algor. (IF 2.1) Pub Date : 2024-02-28 Mark Adams, Paul Muir
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Variance-based stochastic projection gradient method for two-stage co-coercive stochastic variational inequalities Numer. Algor. (IF 2.1) Pub Date : 2024-02-24 Bin Zhou, Jie Jiang, Yongzhong Song, Hailin Sun
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Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors” Numer. Algor. (IF 2.1) Pub Date : 2024-02-23 B. V. Prithvi, S. K. Katiyar
It is the aim of this paper to demonstrate the error in Lemma 1 and Theorem 3 of the contribution from Priyanka et al. (Numer. Algo., 2003). Their novel attempt to study fractal interpolation remains open.
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Continuation Newton methods with deflation techniques for global optimization problems Numer. Algor. (IF 2.1) Pub Date : 2024-02-22 Xin-long Luo, Hang Xiao, Sen Zhang
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An efficient breakdown-free algorithm for numerically evaluating the determinants of (p, q)-pentadiagonal matrices Numer. Algor. (IF 2.1) Pub Date : 2024-02-20 Ji-Teng Jia, Rong Xie, Shuo Ni, Xiao-Yan Xu
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Modified and accelerated relaxed gradient-based iterative algorithms for the complex conjugate and transpose matrix equations Numer. Algor. (IF 2.1) Pub Date : 2024-02-17
Abstract In this paper, by applying the updated technique to the relaxed gradient-based iterative algorithm proposed by Wang et al. (J. Appl. Math. Comput. 67, 317–341 2021), we develop the modified relaxed gradient-based iterative algorithm for the complex conjugate and transpose Sylvester matrix equations. Compared with the relaxed gradient-based iterative algorithm, the modified relaxed gradient-based
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Efficient parametric family of fourth-order Jacobian-free iterative vectorial schemes Numer. Algor. (IF 2.1) Pub Date : 2024-02-15
Abstract In this work, a multiparametric family of iterative vectorial fourth-order methods free of Jacobian matrices is proposed. A convergence analysis of this family is carried out as well as a study of its efficiency. Several numerical experiments are made in order to compare the behaviour of the proposed family with other competitive methods of the literature.
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A fast linearized virtual element method on graded meshes for nonlinear time-fractional diffusion equations Numer. Algor. (IF 2.1) Pub Date : 2024-02-13 Qiling Gu, Yanping Chen, Jianwei Zhou, Jian Huang
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A posteriori error analysis of an ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems Numer. Algor. (IF 2.1) Pub Date : 2024-02-12 Mahboub Baccouch
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Improved uniform error bounds of Lawson-type exponential integrator method for long-time dynamics of the high-dimensional space fractional sine-Gordon equation Numer. Algor. (IF 2.1) Pub Date : 2024-02-10 Junqing Jia, Xiaoyun Jiang, Xiaoqing Chi
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High-order $$L^{2}$$ -bound-preserving Fourier pseudo-spectral schemes for the Allen-Cahn equation Numer. Algor. (IF 2.1) Pub Date : 2024-02-10 Xueqing Teng, Hong Zhang
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ADMM-TGV image restoration for scientific applications with unbiased parameter choice Numer. Algor. (IF 2.1) Pub Date : 2024-02-10 Christian Zietlow, Jörg K. N. Lindner
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A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model Numer. Algor. (IF 2.1) Pub Date : 2024-02-09 Xu Chen, Xin-Xin Gong, Zi-Run She, Zi-Hang She
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Globally linearly convergent nonlinear conjugate gradients without Wolfe line search Numer. Algor. (IF 2.1) Pub Date : 2024-02-09 Arnold Neumaier, Morteza Kimiaei, Behzad Azmi
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A Golub-Welsch version for simultaneous Gaussian quadrature Numer. Algor. (IF 2.1) Pub Date : 2024-02-05 Walter Van Assche
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A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint Numer. Algor. (IF 2.1) Pub Date : 2024-02-03 Xu Liu, Qi Hong, Hong-lin Liao, Yuezheng Gong
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The semi-implicit DLN algorithm for the Navier-Stokes equations Numer. Algor. (IF 2.1) Pub Date : 2024-02-02
Abstract Dahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step methods (the DLN method) that is second order, \(\varvec{A}-\) and \(\varvec{G}-\) stable for arbitrary, non-uniform time steps. Recently, the implementation of the DLN method can be simplified by the refactorization process (adding time filters on the backward Euler scheme). Due to these fine properties, the DLN method