A study on reaction-diffusion singular perturbation problems with non-classical conditions using collocation method

This article discuss about a numerical study to find the solution of second order reaction diffusion singular perturbation problem with non-local boundary conditions using cubic B-spline functions and collocation technique. Shishkin mesh is used to construct layer adapted meshes. The non-local boundary conditions are discretized using Trapezoidal rule. The study establishes that the discussed scheme's result is uniformly convergent up to second order in the supremum norm. To establish the efficiency of the discussed method, two numerical examples are presented along with their results in the form of tables and figures.