Abstract

The present work is devoted to finding numerical solutions of two types of nonlinear integral equations on half line with kernels depending on the sum and difference of arguments. These equations arise in various fields of mathematical physics: kinetic theory of gases, theoretical astrophysics, p-adic string theory, etc. The main result of the work is the derivation of an uniform estimate of the norm of difference between two successive approximations of solutions, which plays an important role for the control of the convergence of iterative schemes and number of iterations. The obtained results have been applied to determine numerical solutions of models from different areas of applications.

中文翻译：

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$$p$$-Adic弦与物理动力学中一些非线性积分方程的数值解

摘要

目前的工作致力于根据参数的和与差来寻找两类带有核的半直线非线性积分方程的数值解。这些方程出现在数学物理的各个领域：气体动力学理论、理论天体物理学、p-进弦理论等。这项工作的主要结果是推导了两个连续近似解之间差异范数的统一估计，对于控制迭代方案的收敛性和迭代次数具有重要作用。获得的结果已用于确定不同应用领域的模型的数值解。