Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume -, Issue -, Pages -Publisher
WILEY
DOI: 10.1002/mma.6772
Keywords
Caputo derivative; boundary layer; tailored finite point method; time fractional convection-diffusion
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Funding
- Natural Science Fund of Shanghai [19ZR1436300]
- National Natural Science Foundation of China [11901266, 11901393]
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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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