Numerical method to solve generalized nonlinear system of second order boundary value problems: Galerkin approach

In this study, we consider the system of second order nonlinear boundary value problems (BVPs). We focus on the numerical solutions of different types of nonlinear BVPs by Galerkin finite element method (GFEM). First of all, we originate the generalized formulation of GFEM for those type of problems. Then we determine the approximate solutions of a couple of second order nonlinear BVPs by GFEM. The approximate results are unfolded in tabuler form and portrayed graphically along with the exact solutions. Those results demonstrate the applicability, compatibility and accuracy of this scheme.