Approximate solution of the multi-term time fractional diffusion and diffusion-wave equations

被引:0
|
作者
Jalil Rashidinia
Elham Mohmedi
机构
[1] Iran University of Science and Technology,School of Mathematics
来源
Computational and Applied Mathematics | 2020年 / 39卷
关键词
Multi-term time fractional diffusion and diffusion-wave equations; Caputo derivative; Legendre collocation method; Convergence analysis; 65M10; 78A48;
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摘要
We develop a numerical scheme for finding the approximate solution for one- and two-dimensional multi-term time fractional diffusion and diffusion-wave equations considering smooth and nonsmooth solutions. The concept of multi-term time fractional derivatives is conventionally defined in the Caputo view point. In the current research, the convergence analysis of Legendre collocation spectral method was carried out. Spectral collocation method is consequently tested on several benchmark examples, to verify the accuracy and to confirm effectiveness of proposed method. The main advantage of the method is that only a small number of shifted Legendre polynomials are required to obtain accurate and efficient results. The numerical results are provided to demonstrate the reliability of our method and also to compare with other previously reported methods in the literature survey.
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