Tailored finite point method for steady-state reaction-diffusion equations

Abstract. In this paper, we propose to use the tailored-finite-point method (TFPM) for a type of steady-state reaction-diffusion problems in two dimensions. Three tailored finite point schemes are constructed for the given problem. Our finite point method has been tailored to some particular properties of the problem. Therefore, our TFPM satisfies the discrete maximum principle automatically. We also study the error estimates of our TFPM. We prove that our TFPM can achieve good accuracy even when the mesh size h≫ ε. Our numerical examples show the efficiency and reliability of our method.

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