An efficient numerical technique for solving nonlinear singularly perturbed reaction diffusion problem

In this paper, a numerical method based on Bernstein polynomial for nonlinear singularly perturbed reaction-diffusion problems is proposed. The solution of this type of problem is polluted by a small positive parameter s along with non-linearity due to which the solution often shows boundary layers, interior layers, and shock waves that arise due to non-linearity. The existence and uniqueness of the solution of the said problems are proved using Nagumo's condition. Moreover, the convergence analysis is carried out of the proposed problem in maximum norm. To illustrate the proposed method's efficiency, three nonlinear test problems have been taken into account, and a comparative analysis has been done with other existing methods. The proposed method's approximated solution seems to be superior or in good agreement with the existing method.