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High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions

Published online by Cambridge University Press:  28 May 2015

Seakweng Vong  and
Zhibo Wang
Seakweng Vong*
Affiliation:
Department of Mathematics, University of Macau, Av. Padre Tomás Pereira Taipa, Macau, China
Zhibo Wang*
Affiliation:
Department of Mathematics, University of Macau, Av. Padre Tomás Pereira Taipa, Macau, China
*
Corresponding author. Email address: [email protected]
Corresponding author. Email address: [email protected]
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Abstract

A compact finite difference scheme is derived for a time fractional differential equation subject to Neumann boundary conditions. The proposed scheme is second-order accurate in time and fourth-order accurate in space. In addition, a high order alternating direction implicit (ADI) scheme is also constructed for the two-dimensional case. The stability and convergence of the schemes are analysed using their matrix forms.

Keywords

65M0665M1265M1535R11Time fractional differential equationNeumann boundary conditionscompact ADI schemeweighted and shifted Grünwald difference operatorconvergence
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 3 , August 2014 , pp. 222 - 241
Copyright
Copyright © Global-Science Press 2014

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