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An efficient parameter uniform spline-based technique for singularly perturbed weakly coupled reaction-diffusion systems
  • Satpal Singh,
  • Devendra Kumar,
  • HIGINIO RAMOS
Satpal Singh
Birla Institute of Technology and Science Pilani

Corresponding Author:satpalsingh1704@gmail.com

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Devendra Kumar
Birla Institute of Technology and Science
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HIGINIO RAMOS
UNIVERSIDAD DE SALAMANCA
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Abstract

A parameter-uniform numerical scheme for a system of weakly coupled singularly perturbed reaction-diffusion equations of arbitrary size with appropriate boundary conditions is investigated. More precisely, quadratic $B$-spline basis functions with an exponentially graded mesh are used to solve a $\ell\times\ell$ system whose solution exhibits parabolic (or exponential) boundary layers at both endpoints of the domain. A suitable mesh generating function is used to generate the exponentially graded mesh. The decomposition of the solution into regular and singular components is obtained to provide error estimates. A convergence analysis is addressed, which shows a uniform convergence of the second order. To validate the theoretical findings, two test problems are solved numerically.