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Volume 5, Issue 1
Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation

Jincheng Ren & Zhi-Zhong Sun

East Asian J. Appl. Math., 5 (2015), pp. 1-28.

Published online: 2018-02

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  • Abstract

Some efficient numerical schemes are proposed to solve one-dimensional and two-dimensional multi-term time fractional diffusion-wave equation, by combining the compact difference approach for the spatial discretisation and an $L1$ approximation for the multi-term time Caputo fractional derivatives. The unconditional stability and global convergence of these schemes are proved rigorously, and several applications testify to their efficiency and confirm the orders of convergence.

  • AMS Subject Headings

65M06, 65M12, 65M15

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-1, author = {}, title = {Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {1}, pages = {1--28}, abstract = {

Some efficient numerical schemes are proposed to solve one-dimensional and two-dimensional multi-term time fractional diffusion-wave equation, by combining the compact difference approach for the spatial discretisation and an $L1$ approximation for the multi-term time Caputo fractional derivatives. The unconditional stability and global convergence of these schemes are proved rigorously, and several applications testify to their efficiency and confirm the orders of convergence.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080714.031114a}, url = {http://global-sci.org/intro/article_detail/eajam/10775.html} }
TY - JOUR T1 - Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 28 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.080714.031114a UR - https://global-sci.org/intro/article_detail/eajam/10775.html KW - Multi-term time fractional diffusion-wave equation, compact difference scheme, discrete energy method, convergence. AB -

Some efficient numerical schemes are proposed to solve one-dimensional and two-dimensional multi-term time fractional diffusion-wave equation, by combining the compact difference approach for the spatial discretisation and an $L1$ approximation for the multi-term time Caputo fractional derivatives. The unconditional stability and global convergence of these schemes are proved rigorously, and several applications testify to their efficiency and confirm the orders of convergence.

Jincheng Ren & Zhi-Zhong Sun. (1970). Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation. East Asian Journal on Applied Mathematics. 5 (1). 1-28. doi:10.4208/eajam.080714.031114a
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