Differentiability properties of solutions of the equation -ε2δ u + ru=f(x,y) in a square
SIAM Journal on Mathematical Analysis
Applied Numerical Mathematics
A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems
Applied Numerical Mathematics
High Order varepsilon-Uniform Methods for Singularly Perturbed Reaction-Diffusion Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
Uniform Convergence of Finite-Difference Schemes for Reaction-Diffusion Interface Problems
Large-Scale Scientific Computing
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In this work we define a compact finite difference scheme of positive type to solve a class of 2D reaction-diffusion elliptic singularly perturbed problems. We prove that if the new scheme is constructed on a piecewise uniform mesh of Shishkin type, it provides better approximations than the classical central finite difference scheme. Moreover, the uniform parameter bound of the error shows that the scheme is third order convergent in the maximum norm when the singular perturbation parameter is sufficiently small. Some numerical experiments illustrate in practice the result of convergence proved theoretically.