Volume 9, Issue 3
Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain

Gongsheng Li, Chunlong Sun, Xianzheng Jia & Dianhu Du

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 337-357.

Published online: 2016-09

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  • Abstract

This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo's definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and convergence are proved. The numerical results demonstrate the effectiveness of the theoretical analysis, and the method and technique can also be applied to other kinds of time/space fractional diffusion equations.

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@Article{NMTMA-9-337, author = {}, title = {Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {3}, pages = {337--357}, abstract = {

This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo's definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and convergence are proved. The numerical results demonstrate the effectiveness of the theoretical analysis, and the method and technique can also be applied to other kinds of time/space fractional diffusion equations.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.y13024}, url = {http://global-sci.org/intro/article_detail/nmtma/12380.html} }
TY - JOUR T1 - Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 337 EP - 357 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.y13024 UR - https://global-sci.org/intro/article_detail/nmtma/12380.html KW - AB -

This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo's definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and convergence are proved. The numerical results demonstrate the effectiveness of the theoretical analysis, and the method and technique can also be applied to other kinds of time/space fractional diffusion equations.

Gongsheng Li, Chunlong Sun, Xianzheng Jia & Dianhu Du. (2020). Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain. Numerical Mathematics: Theory, Methods and Applications. 9 (3). 337-357. doi:10.4208/nmtma.2016.y13024
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