Tailored finite point method for time fractional convection dominated diffusion problems with boundary layers

We propose a tailored finite point method (TFPM) for solving time fractional convection dominated diffusion equations in this paper. The main idea of TFPM is to firstly approximate the diffusion, convection coefficient near each grid by a constant, and then determine the weights of the finite differ...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 47; no. 13; pp. 11044 - 11061
Main Authors Wang, Yihong, Cao, Jianxiong, Fu, Junliang
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.09.2024
Subjects
boundary layer
Boundary layer stability
Boundary layer transition
Caputo derivative
Convection
Diffusion layers
Exact solutions
Finite difference method
Mathematical analysis
tailored finite point method
time fractional convection‐diffusion
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ISSN0170-4214
1099-1476
DOI10.1002/mma.6772

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Summary:We propose a tailored finite point method (TFPM) for solving time fractional convection dominated diffusion equations in this paper. The main idea of TFPM is to firstly approximate the diffusion, convection coefficient near each grid by a constant, and then determine the weights of the finite difference scheme by using the exact solution of the convection diffusion equation with constant coefficients. This adaptation perfectly captures the rapid transition of the solutions which contain sharp boundary layers even with coarse meshes. The accuracy and stability of the scheme are rigorously analyzed. Numerical examples are shown to verify the accuracy and reliability of the proposed scheme.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6772