SIAM Journal on Numerical Analysis
A computational method for solving singular perturbation problems
Applied Mathematics and Computation
Applied Mathematics and Computation
Journal of Optimization Theory and Applications
A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems
The Journal of Supercomputing
An efficient hybrid numerical scheme for convection-dominated boundary-value problems
International Journal of Computer Mathematics - RECENT ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
A numerical method for singularly perturbed turning point problems with an interior layer
Journal of Computational and Applied Mathematics
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This article presents a numerical method to solve singularly perturbed turning point problems exhibiting two exponential boundary layers. Classical finite-difference schemes do not yield parameter uniform convergent results on a uniform mesh, in general (Robust Computational Techniques for Boundary Layers, Chapman & Hall, London, CRC Press, Boca Raton, FL, 2000). In order to overcome this difficulty, we propose an appropriate piecewise uniform (Shishkin) mesh and apply the classical finite-difference schemes on this mesh. Error estimates are derived by decomposing the solution into smooth and singular components. The present method is layer resolving as well as parameter uniform convergent. Numerical examples are presented to show the applicability and efficiency of the method.