Stability and convergence analysis on Shishkin mesh for a nonlinear singularly perturbed problem with three-point boundary condition

Abstract

The present study is conducted on finite difference method in Shishkin piecewise uniform mesh in a singularly perturbed boundary value problem for a nonlinear differential equation. Then, stability and convergence analysis are given for the difference scheme in the discrete maximum norm and is determined that uniformly convergent in perturbation parameter. Finally, an example is presented to support the theoretical findings and the results are presented in tables and graphs.