A New Error Evaluation for Singularly Perturbed Problem with Multi-Point Boundary Condition

We consider finite difference method to find best approximation of nonlinear singularly perturbed problem which contains multi-point boundary conditions. We surveyed the asymptotic estimates of the corresponding problem that needs to be solved with maximum principle. We constructed a finite difference scheme by using Bakhvalov mesh. Based on the error estimation, we proved that this method was first-order, uniformly convergent method with in the discrete maximum norm. Finally, we conducted a numerical experiment in order to check the theoretical results

Keywords:

Singular perturbation , finite difference scheme , Bakhvalov mesh , Uniformly convergence , multipoint boundary conditions