Domain decomposition in boundary layers for singularly perturbed problems
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems
The Journal of Supercomputing
A computational method for self-adjoint singular perturbation problems using quintic spline
Computers & Mathematics with Applications
Parallelizable computational technique for singularly perturbed boundary value problems using spline
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
A parallel approach for self-adjoint singular perturbation problems using Numerov's scheme
International Journal of Computer Mathematics
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In this paper, a parallelizable computational technique for singularly perturbed reaction-diffusion problems is analyzed and implemented on parallel computer. In this technique, the domain is decomposed into non-overlapping subdomains, and boundary value problems are posed on each subdomain with suitable boundary conditions. Then, each problem is solved by the adaptive spline based difference scheme on each subinterval on parallel computer. Detailed theoretical analysis is provided to prove the convergence of the technique. To check the validity of the method, parallel implementation is performed on a numerical example and results are presented.