Numerical simulation of an anomalous diffusion process based on the higher-order accurate scheme

L. I. Moroz ; A. G. Maslovskaya

Matematičeskoe modelirovanie, Tome 32 (2020) no. 10, pp. 62-76.

Résumé

The paper is devoted to the development and program implementation of a computational algorithm for modeling a process of anomalous diffusion. The mathematical model is formulated as an initial-boundary value problem for a nonlinear fractional order partial differential equation. An implicit finite-difference scheme based on an increased accuracy order approximation for the Caputo derivative is constructed. An application program was designed to perform computer simulation of the anomalous diffusion process. The numerical analysis of the accuracy of approximate solutions is conducted using a test-problem. The results of computational experiments are presented on the example of the modeling of a fractal nonlinear dynamic reaction-diffusion system.

Détail

Mots-clés : anomalous diffusion equation, reaction-diffusion process
Keywords: Caputo fractional derivative, implicit finite difference scheme.

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