An accelerated numerical computation for singularly perturbed Robin-type parabolic problems with small parameters

This study presents a computational method for solving singularly perturbed Robin-type parabolic problem with two perturbation parameters. The fitted operator method in the space direction and the implicit Euler approach in the time direction are used to discretize the problem on a uniform mesh. Furthermore, the new fitted operator method is used to discretize the Robin boundary conditions. The linear order of parameter-uniform convergence has been investigated in both the time and space variables. The application of the Richardson extrapolation approach enhanced the accuracy and rate of convergence of the present method from linear to quadratic order. On the computations of two numerical examples, the theoretical and computational results agreed upon.