Abstract
In this paper, we propose a class of new tailored finite point methods (TFPM) for the numerical solution of parabolic equations. Our finite point method has been tailored based on the local exponential basis functions. By the idea of our TFPM, we can recover all the traditional finite difference schemes. We can also construct some new TFPM schemes with better stability condition and accuracy. Furthermore, combining with the Shishkin mesh technique, we construct the uniformly convergent TFPM scheme for the convection-dominant convection-diffusion problem. Our numerical examples show the efficiency and reliability of TFPM.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11322113
Award Identifier / Grant number: 91330203
Funding statement: This work was partially supported by the NSFC projects 11322113 and 91330203, and the Sino-German Science Center (Grant ID 1228) on the occasion of the Chinese-German Workshop on Computational and Applied Mathematics in Augsburg 2015.
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