Cubic spline scheme on variable mesh for singularly perturbed periodical boundary value problem. (English) Zbl 1462.65089
Summary: In this paper, a numerical method is suggested to solve singularly perturbed periodical boundary value problem for linear second order ordinary differential equation with a small parameter multiplying the first and second derivatives. This method involves a cubic spline scheme along with non-uniform meshes to the above said problem so as to derive the scheme is second order accurate in the maximum norm. The theoretical results are validated through numerical experiments.
MSC:
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
Keywords:
singular perturbation; periodical boundary value problem; variable mesh; boundary layers; cubic spline schemeReferences:
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