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High‐order compact finite difference method for the multi‐term time fractional mixed diffusion and diffusion‐wave equation
Author(s) -
Yu Bo
Publication year - 2021
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.7207
Subject(s) - mathematics , compact finite difference , finite difference method , diffusion equation , finite difference , norm (philosophy) , finite difference coefficient , convergence (economics) , diffusion , stability (learning theory) , mathematical analysis , finite element method , mixed finite element method , physics , computer science , quantum mechanics , machine learning , economic growth , political science , law , economics , thermodynamics , service (business) , economy
In this paper, the multi‐term time fractional mixed diffusion and diffusion‐wave equation is investigated. Firstly, a compact finite difference scheme with fourth‐order spatial accuracy and high‐order temporal accuracy is derived. Then, the unconditional stability and convergence in the maximum norm of the derived high‐order compact finite difference method have been discussed rigorously by means of the energy method. Numerical experiments are presented to test the convergence order in the temporal and spatial direction, respectively. Additionally, to precisely demonstrate the computational efficiency of the derived high‐order compact finite difference method, the maximum norm error and the CPU time are measured in contrast with the second‐order finite difference scheme for the same temporal grid size. Finally, a practical example is presented to show the applicability of the time fractional mixed diffusion and diffusion‐wave model and the efficiency of the derived high‐order compact finite difference method.