Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume -, Issue -, Pages -Publisher
SPRINGEROPEN
DOI: 10.1186/1687-1847-2012-8
Keywords
multi-term FDEs; multi-point boundary conditions; tau method; collocation method; direct method; shifted Legendre polynomials; Gauss-Lobatto quadrature
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Funding
- Northern Border University [035/432]
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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.
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