A robust spline difference method for robin-type reaction-diffusion problem using grid equidistribution

Aastha Gupta and Aditya Kaushik

Applied Mathematics and Computation, 2021, vol. 390, issue C

Abstract: 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.

Keywords: Singularly perturbed boundary value problems; Robin-type reaction-diffusion problems; Grid equidistribution; Spline difference scheme; Cubic and exponential splines; Parameter-uniform discretization (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:390:y:2021:i:c:s009630032030552x

DOI: 10.1016/j.amc.2020.125597

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