Parameter-uniform approximation on equidistributed meshes for singularly perturb e d parabolic reaction-diffusion problems with Robin boundary conditions

In this work we develop a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions. The discretization consists of a modified Euler scheme in time, a central difference scheme in space, and a special finite difference scheme for the Robin boundary conditions. A uniform mesh is used in the time direction while the mesh in the space direction is generated via the equidistribution of a suitably chosen monitor function. We discuss error analysis and prove that the method is parameter-uniformly convergent of order two in space and order one in time. To support the theoretical result, some numerical experiments are performed. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

The paper presents a parameter-uniform numerical method for solving singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions, using a modified Euler scheme in time, a central difference scheme in space, and a special finite difference scheme for the boundary conditions. The method is proven to converge of order two in space and order one in time, with numerical experiments supporting the theoretical results.