An alternating direction implicit spectral method for two-dimensional multi-term time-space fractional diffusion-wave equations
Yong-Suk Kang1, Chu-Myong Ri1, Chol-Guk Choe2,3
1Kim Il Sung University, Pyongyang, Pyongyang, Democratic People's Republic of Korea
2Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea
3University of Science and Technology Beijing, Beijing, China
Keywords: alternating direction implicit method, Legendre spectral method, multi-term time fractional-Riesz space fractional diffusion-wave equation, stability and convergence
Abstract
In this paper, we consider two-dimensional multi-term time-space fractional diffusion-wave equations. We develop an alternating direction implicit (ADI) spectral method based on Legendre spectral approximation in space and finite difference discretization in time. We also prove the numerical stability and convergence of the developed scheme and that the error is O(τ2+Nγ-r), where Ν,τ,γ,r are the polynomial degree, time step size, Riesz derivative order and the regularity of the exact solution, respectively.
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