求解带积分边界条件的奇异扰动 Volterra-Fredholm 积分微分方程的拟合近似法

Pub Date : 2024-07-30 DOI:10.1007/s11253-024-02312-z

Baransel Gunes, Musa Cakir

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引用次数: 0

摘要

我们考虑了一种新的数值方法，用于求解具有层行为和积分边界条件的二阶 Volterra-Fredholm 微分方程的边界值问题。在合适的 Shishkin 型网格上提出了一种有限差分方案，以获得所提问题的近似解。研究证明，该方法在离散最大规范下具有一阶收敛性。两个数值示例展示了该方法的效率。

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A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition

We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.

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