奇异扰动 Volterra 迟滞积分微分方程的巴赫瓦洛夫型网格上的二阶差分方案

IF 2.6 3区数学 Computational and Applied Mathematics Pub Date : 2024-07-31 DOI:10.1007/s40314-024-02873-6

Yige Liao, Xianbing Luo, Li-Bin Liu

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摘要

本文提出了一种在巴赫瓦洛夫网格上处理奇异扰动 Volterra 延迟积分微分方程的二阶参数均匀数值方法。方程的离散化采用了一阶导数项的可变两步反向微分公式和积分项的梯形公式。证明了离散最大规范数值方法的稳定性和收敛性。最后，通过一些数值实验验证了理论结果。

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A second order difference scheme on a Bakhvalov-type mesh for the singularly perturbed Volterra delay-integro-differential equation

In this paper, we present a second order parameter-uniform numerical method for a singularly perturbed Volterra delay-integro-differential equation on a Bakhvalov-type mesh. The equation is discretized by using the variable two-step backward differentiation formula of the first derivative term and the trapezoidal formula of the integral term. The stability and convergence of the numerical method in the discrete maximum norm are proved. Finally, the theoretical results are verified by some numerical experiments.

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来源期刊

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.