二阶中性伏特拉积分微分方程的数值解法：稳定性分析和有限差分法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-11-10 DOI:10.1016/j.cam.2024.116371

Burcu Fedakar , Ilhame Amirali , Muhammet Enes Durmaz , Gabil M. Amiraliyev

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引用次数: 0

摘要

本研究涉及二阶中性 Volterra 积分微分方程的初值问题。首先，我们给出了稳定性不等式，表明问题在右边和初始条件方面的稳定性。此外，我们还开发了一种有限差分法，该方法在微分部分使用二阶差分导数，在积分部分使用适当的复合梯形和中点矩形规则，并在中间点使用二阶精确差分量。建立了近似解的误差估计。为支持理论结果，采用所提出的数值技术进行了数值计算。

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Numerical solutions for second-order neutral volterra integro-differential equations: Stability analysis and finite difference method

This work deals with the initial-value problem for a second-order neutral Volterra integro-differential equation. First, we give the stability inequality indicating stability of the problem with respect to the right-side and initial conditions. Further, we develop a finite difference method that uses for differential part second difference derivative, for the integral part appropriate composite trapezoidal and midpoint rectangle rules followed by second-order accurate difference quantities at intermediate points. Error estimate for the approximate solution is established. In support of theoretical results, numerical results are performed by employing the proposed numerical technique.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.