The parameter uniform numerical method for singularly perturbed parabolic reaction-diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction-diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter-uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.