文章基本信息

标题：A shifted Legendre spectral method for fractional-order multi-point boundary value problems
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作者：Ali H Bhrawy ; Mohammed M Al-Shomrani
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2012
卷号：2012
期号：1
页码：8
DOI：10.1186/1687-1847-2012-8
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this article, a shifted Legendre tau method is introduced to get a direct solution technique for solving multi-order fractional differential equations (FDEs) with constant coefficients subject to multi-point boundary conditions. The fractional derivative is described in the Caputo sense. Also, this article reports a systematic quadrature tau method for numerically solving multi-point boundary value problems of fractional-order with variable coefficients. Here the approximation is based on shifted Legendre polynomials and the quadrature rule is treated on shifted Legendre Gauss-Lobatto points. We also present a Gauss-Lobatto shifted Legendre collocation method for solving nonlinear multi-order FDEs with multi-point boundary conditions. The main characteristic behind this approach is that it reduces such problem to those of solving a system of algebraic equations. Thus we can find directly the spectral solution of the proposed problem. Through several numerical examples, we evaluate the accuracy and performance of the proposed algorithms.
关键词：multi-term FDEs ; multi-point boundary conditions ; tau method ; collocation method ; direct method ; shifted Legendre polynomials ; Gauss-Lobatto quadrature.