A NUMERICAL SOLUTION STUDY ON SINGULARLY PERTURBED CONVECTION-DIFFUSION NONLOCAL BOUNDARY PROBLEM

Abstract

This important numerical method is given for the numerical solution of singularly perturbed convection-di§usion nonlocal boundary valueproblem. First, the behavior of the exact solution is analyzed, which is neededfor analysis of the numerical solution in later sections. Next, uniformly convergent Önite di§erence scheme on a Shishkin mesh is established, which is basedon the method of integral identities with the use exponential basis functionsand interpolating quadrature rules with weight and remainder term in integralform. It is shown that the method is Örst order accurate expect for a logarithmic factor, in the discrete maximum norm. Finally, the numerical resultsare presented in table and graphs, and these results reveal the validity of thetheoretical results of our method.