A finite difference method for an anomalous sub-diffusion equation, theory and applications

Autor:	Kassem Mustapha, Jaafar AlMutawa
Rok vydání:	2012
Předmět:	Diffusion equation Exact solutions in general relativity Series (mathematics) Discretization Applied Mathematics Numerical analysis Mathematical analysis Finite difference Finite difference method Finite difference coefficient Mathematics
Zdroj:	Numerical Algorithms. 61:525-543
ISSN:	1572-9265 1017-1398
DOI:	10.1007/s11075-012-9547-0
Popis:	The numerical solution for a class of fractional sub-diffusion equations is studied. For the time discretization, we use a generalized Crank–Nicolson method combined with the second central finite difference (FD) for the spatial discretization which will then define a fully discrete implicit FD scheme. An error of order O(h2 max (1, log k − 1) + k2 + α) has been shown where h and k denote the maximum space and time steps, respectively. A non-uniform time step is employed to compensate for the singular behaviour of the exact solution at t = 0. Our theoretical results are numerically validated in a series of test problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::81a0364ee1e494a7932b88bcafe4c00f https://doi.org/10.1007/s11075-012-9547-0 Zobrazit plný text záznamu Full text from SpringerLink