期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 228, 期 8, 页码 3137-3153出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.01.014
关键词
Fractional partial differential equations; Differential equations with delays; Fractional diffusion equation; Numerical methods; Discretization
资金
- Department of Electrical and Computer Engineering of the Utah State University [SAB2006-0172]
- [LPP-0283-06]
- [APVV-0040-07]
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359-386]. Four examples of numerical solution of fractional diffusion equation with various combinations of time-/space-fractional derivatives (integer/integer, fractional/integer, integer/fractional. and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed. (C) 2009 Elsevier Inc. All rights reserved,
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