A singularly perturbed model problem for numerical computation
Journal of Computational and Applied Mathematics
Analysis of a cell-vertex finite volume method for convection-diffusion problems
Mathematics of Computation
Journal of Computational Physics
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
A Tailored Finite Point Method for a Singular Perturbation Problem on an Unbounded Domain
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 type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small 驴, i.e. the boundary layers and interior layers do not need to be resolved numerically. In our numerical implementation, we study the classification of all the singular points for the corresponding degenerate first order linear dynamic system. We also study some cases with nonlinear coefficients. Our tailored finite point method is very efficient in both linear and nonlinear coefficients cases.