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

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  • Gupta, Aastha
  • Kaushik, Aditya

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.

Suggested Citation

  • Gupta, Aastha & Kaushik, Aditya, 2021. "A robust spline difference method for robin-type reaction-diffusion problem using grid equidistribution," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s009630032030552x
    DOI: 10.1016/j.amc.2020.125597
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