In this paper, numerical solution for singularly perturbed problem with nonlocal boundary conditions is obtained. Finite difference method used to discretize on the Bakhvalov-Shishkin mesh. The some properties of exact are analyzed. error obtained first-order in discrete maximum norm. Finally, an example solved show advantages finite method.

• We consider the reaction diffusion problem for singular perturbed case when term dominates equation. Using optimal test norm and SP reformulation, we provide efficient discretization processes. present a preconditioning strategy that works large range of perturbation parameter. introduce simplified Bramble-Pasciak-Vassilevski type preconditioner. ways to discretize precondition in concepts sa...