Differentiability properties of solutions of the equation -ε2δ u + ru=f(x,y) in a square
SIAM Journal on Mathematical Analysis
SIAM Journal on Numerical Analysis
A compact finite difference scheme for 2D reaction-diffusion singularly perturbed problems
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
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We consider a singularly perturbed reaction-diffusion equation in two dimensions (x,y) with concentrated source on a segment parallel to axis Oy. By means of an appropriate (including corner layer functions) decomposition, we describe the asymptotic behavior of the solution. Finite difference schemes for this problem of second and fourth order of local approximation on Shishkin mesh are constructed. We prove that the first scheme is almost second order uniformly convergent in the maximal norm. Numerical experiments illustrate the theoretical order of convergence of the first scheme and almost fourth order of convergence of the second scheme.