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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*
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: swvong@umac.mo
Corresponding author. Email address: zhibowangok@gmail.com
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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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2014

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