A singularly perturbed model problem for numerical computation
Journal of Computational and Applied Mathematics
Error Estimates for the Finite Element Approximation of Problems in Unbounded Domains
SIAM Journal on Numerical Analysis
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Journal of Scientific Computing
A Tailored Finite Point Method for Convection-Diffusion-Reaction Problems
Journal of Scientific Computing
Journal of Scientific Computing
Tailored Finite Point Method for First Order Wave Equation
Journal of Scientific Computing
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In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [2005]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small 驴. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh.