A parameter uniform B-spline collocation method for solving singularly perturbed turning point problem having twin boundary layers. (English) Zbl 1236.65092
For singularly perturbed two-point boundary value problems, bounds for the solution and its derivatives are established, and a B-spline collocation method on Shishkin meshes is proposed for numerical approximation. Stability and convergence estimates in the maximum norm are derived, showing convergence of order 2 up to a logarithmic factor. Numerical examples demonstrate both the accuracy and the convergence order of the proposed numerical method.
Reviewer: M. Plum (Karlsruhe)
MSC:
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |
34E15 | Singular perturbations for ordinary differential equations |
65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |