A robust spline difference method for Robin-type reaction-diffusion problem using grid equidistribution. (English) Zbl 1508.65088
Summary: This paper presents a numerical approximation technique to solve reaction-diffusion singularly-perturbed differential equation with robin-type boundary conditions. The proposed technique applies cubic splines to discretize the robin-boundary conditions and exponential splines to generate the solution of singularly perturbed differential equation at the internal nodes of a layer adapted grid. The layer adapted grid is generated by equidistributing a positive monitor function. The error estimates indicate that the proposed technique is parameter-uniform second-order convergent and is numerically stable. Numerical experiments have been performed and presented to corroborate the theoretical results.
MSC:
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
Keywords:
singularly perturbed boundary value problems; Robin-type reaction-diffusion problems; grid equidistribution; spline difference scheme; cubic and exponential splines; parameter-uniform discretizationReferences:
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