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The Galerkin spectral element method for the solution of two‐dimensional multiterm time fractional diffusion‐wave equation
Author(s) -
Saffarian Marziyeh,
Mohebbi Akbar
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6049
Subject(s) - mathematics , legendre polynomials , stability (learning theory) , galerkin method , mathematical analysis , diffusion , spectral method , diffusion equation , wave equation , element (criminal law) , scheme (mathematics) , numerical analysis , work (physics) , finite element method , physics , computer science , law , political science , economics , thermodynamics , service (business) , economy , machine learning
The aim of this work is to propose an efficient numerical method for the solution of two‐dimensional multiterm time fractional diffusion‐wave equation. The Caputo time fractional derivatives of equation are approximated by a scheme of order O ( τ 3 − α ) , 1< α <2. To obtain a full‐discrete scheme, we apply the Legendre spectral element method on the spatial direction. Unconditional stability of the semidiscrete scheme and error estimate of full‐discrete method is presented. Numerical experiments are carried out to demonstrate the accuracy of the proposed method and to compare the results with the numerical solutions of other schemes in the literature. The results show that the present method is accurate and efficient. It is illustrated that the numerical results are in good agreement with theoretical ones.