非线性非局部边界条件下扩散方程的一种修正后向欧拉格式

Pub Date : 2021-09-25 DOI:10.32523/2306-6172-2021-9-3-26-38

Dehilis Sofiane, Bouziani Abdelfatah, Bensaid Souad

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引用次数: 0

摘要

本文提出了求解非线性非局部边界条件下扩散方程的修正后向欧拉格式。该方案是通过结合空间中的四阶紧致有限差分公式和时间导数项的后向差分来导出的。边界条件中的非线性项用泰勒展开法线性化。通过算例验证了该方法的准确性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A MODIFIED BACKWARD EULER SCHEME FOR THE DIFFUSION EQUATION SUBJECT TO NONLINEAR NONLOCAL BOUNDARY CONDITIONS

In this article, Modified Backward Euler Scheme is developed to solve the diffusion equation subject to nonlinear nonlocal boundary conditions. The proposed scheme is derived by combining a fourth-order compact finite difference formula in space and a backward differ- entiation for the time derivative term. Nonlinear terms in boundary conditions are linearized by Taylor expansion. Numerical examples are provided to verify the accuracy and efficiency of our proposed method.

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