SIAM Journal on Numerical Analysis
semilinear boundry value problem, singular peturbation, finite-difference scheme, piecewise uniform mesh
Boundary value problems for singularly perturbed semilinear elliptic equations are considered. Special piecewise-uniform meshes are constructed which yield accurate numerical solutions irrespective of the value of the small parameter. Numerical methods composed of standard monotone finite difference operators and these piecewise-uniform meshes are shown theoretically to be uniformly (with respect to the singular perturbation parameter) convergent. Numerical results are also presented, which indicate that in practice the method is first-order accurate.
Farrell, Paul A.; Miller, John J. H.; O'Riordan, Eugene; and Shishkin, Grigori I. (1996). A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation. SIAM Journal on Numerical Analysis 33(3), 1135-1149. Retrieved from https://digitalcommons.kent.edu/cspubs/13