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

High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions
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Year:    2014

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 222–241

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.281013.300414a

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 222–241

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Time fractional differential equation Neumann boundary conditions compact ADI scheme weighted and shifted Grunwald difference operator convergence.

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