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Volume 4, Issue 3
High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions

Seakweng Vong & Zhibo Wang

DOI: 10.4208/eajam.281013.300414a

East Asian J. Appl. Math., 4 (2014), pp. 222-241.

Published online: 2018-02

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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

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

  • AMS Subject Headings

65M06, 65M12, 65M15, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-222, author = {Seakweng Vong and Zhibo Wang}, title = {High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.281013.300414a}, url = {http://global-sci.org/intro/article_detail/eajam/10834.html} }
TY - JOUR T1 - High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions AU - Seakweng Vong & Zhibo Wang JO - East Asian Journal on Applied Mathematics VL - 3 SP - 222 EP - 241 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.281013.300414a UR - https://global-sci.org/intro/article_detail/eajam/10834.html KW - Time fractional differential equation, Neumann boundary conditions, compact ADI scheme, weighted and shifted Grunwald difference operator, convergence. AB -

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.

Seakweng Vong and Zhibo Wang. (2018). High Order Difference Schemes for a Time Fractional Differential Equation with Neumann Boundary Conditions. East Asian Journal on Applied Mathematics. 4 (3). 222-241. doi:10.4208/eajam.281013.300414a
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