非线性反应扩散系统的一种具有维数分裂的四阶指数差分格式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-02-21 DOI:10.1016/j.cam.2025.116568

E.O. Asante-Asamani , A. Kleefeld , B.A. Wade

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引用次数: 0

摘要

提出了一种具有维数分裂的四阶指数时差（ETD）龙格-库塔格式，用于求解多维非线性反应扩散方程组。通过用a可接受的pad(2,2)有理函数逼近格式中的矩阵指数，经验验证了所得格式（ETDRK4P22-IF）对多个RDE具有四阶精度。该方案被证明比竞争的四阶ETD和IMEX方案更有效，在CPU时间上实现了高达20倍的加速。包含多达三个低阶l -稳定格式的预平滑步骤，有助于有效地阻尼由非光滑初始/边界条件问题引起的杂散振荡。

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A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction–diffusion systems

A fourth-order exponential time differencing (ETD) Runge–Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction–diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Padé (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20X speed-up in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.

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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.