Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation

Publication Year

2010

Journal Title

Journal of Computational Physics

Volume number

229

Issue number

18

Publisher

Elsevier

First Page (page number)

6613

Last Page (page number)

6622

Referreed

1

DOI

10.1016/j.jcp.2010.05.015

ISSN (print)

00219991

Keywords

Fractional differential equations, Kansa’s method, radial basis functions, collocation, adaptive greedy algorithm, geometric time grids

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