A robust numerical technique for weakly coupled system of parabolic singularly perturbed reaction–diffusion equations

摘要

Abstract This article presents a uniformly convergent numerical technique for a time-dependent reaction-dominated singularly perturbed system, including the same diffusion parameters multiplied with second-order spatial derivatives in all equations. Boundary layers are observed in the solution components for the small parameter. The proposed numerical technique consists of the Crank–Nicolson scheme in the temporal direction over a uniform mesh and quadratic Bdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {B}$$end{document}-splines collocation technique over an exponentially graded mesh in the spatial direction. We derived the robust error estimates to establish the optimal order of convergence. Numerical investigations confirm the theoretical determinations and the proposed method’s efficiency and accuracy.