Numerical treatment of an initial-boundary value problem for fractional partial differential equations

Details Numerical treatment of an initial-boundary value problem for fractional partial differential equations Numerical treatment of an initial-boundary value problem for fractional partial differential equations

2006-07-05

arxiv.org/abs/math/0607103v2

Signal Processing, Volume 86, Issue 10, October 2006, Pages 2619-2631

Mathematics

Numerical Analysis

18 pages, 4 figures

Scientific paper

10.1016/j.sigpro.2006.02.009

This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view, the equation includes at least two fractional derivatives: spatial and temporal. In this paper we proposed a new numerical scheme for the spatial derivative, the so called Riesz-Feller operator. Moreover, using the finite difference method, we show how to employ this scheme in the numerical solution of fractional partial differential equations. In other words, we considered an initial-boundary value problem in one dimensional space. In the final part of this paper some numerical results and plots of simulations are shown as examples.

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