Singular perturbation methods for ordinary differential equations
Singular perturbation methods for ordinary differential equations
Applied Numerical Mathematics
Booster method for singularly-perturbed one-dimensional convection-diffusion Neumann problems
Journal of Optimization Theory and Applications
Applied Mathematics and Computation
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems
The Journal of Supercomputing
An efficient numerical method for singular perturbation problems
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
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This article presents a numerical scheme for convection-dominated two-point boundary-value problems. The proposed scheme combines the cubic spline scheme and the midpoint scheme in an appropriate manner. In the inner region, the convective term is approximated by three-point differences by spline approximation of solution at the mesh points, whereas in the outer region the midpoint approximations are used for convective term, and the classical central difference scheme is used for the diffusive term. The first-order derivative in the left boundary point is approximated by the cubic spline. This scheme is applied on the boundary layer resolving Shishkin mesh. Truncation error is derived, and the proposed method is applied to couple of examples to show its accuracy and efficiency.