Crank-Nicolson ADI Finite Difference Method for Three-Dimensional Nonlinear Partial Integro-Differential Equations with Weak Singular Kernels
Year: 2025
Author: Yanping Chen, Ruru Wang, Leijie Qiao
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 4 : pp. 867–889
Abstract
The main objective of this study is to present a fast and efficient numerical scheme for solving nonlinear integral differential equations with weak singular kernels in three-dimensional domain. First, the temporal derivative and integral term are approximated by the Crank-Nicolson (CN) method and the second-order fractional quadrature rule. After that the spatial discretization is carried out by combining the finite difference method and the alternating direction implicit (ADI) method, and the nonlinear term are approximated using the Taylor expansion. The stability and convergence of the proposed scheme are analyzed, followed by the verification of the theoretical results through numerical experiments.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2024-088.301024
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 4 : pp. 867–889
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Three-dimensional nonlinear integral differential equation alternating direction implicit method finite difference method stability convergence.