On modeling of semilinear singularly perturbed reaction-diffusion problem
Nonlinear Analysis: Theory, Methods & Applications
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
A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems
The Journal of Supercomputing
Quintic Spline Based Computational Scheme for Singularly Perturbed Convection-Diffusion Problems
HPCS '05 Proceedings of the 19th International Symposium on High Performance Computing Systems and Applications
A computational method for self-adjoint singular perturbation problems using quintic spline
Computers & Mathematics with Applications
Parallel implementation of a spline based computational approach for singular perturbation problems
HiPC'06 Proceedings of the 13th international conference on High Performance Computing
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In this paper, we considered singularly perturbed self-adjoint boundary-value problems and proposed a computational technique based on Numerov's scheme, which is also suitable for parallel computing. The whole domain is divided into three non-overlapping subdomains, and corresponding subproblems are obtained by using zeroth-order approximations of the solution at the boundaries of these subproblems. The subproblems corresponding to boundary-layer regions are solved using Numerov's method after the introduction of suitable stretching variables and the solution of the reduced problem is taken as an approximate solution in the outer region. A numerical example is provided to show the efficiency and accuracy of the technique.