one step hybrid block method for solving nonlinear second order dirichlet value problems of ordinary differential equations directly

The aim of this article is to approximate the solution of nonlinear second-order dirichlet boundary value problems of ordinary differential equations directly using the hybrid block method. to derive this method, we first transform the boundary value problem to its corresponding second-order initial value problem via the nonlinear shooting method. then, a direct one-step hybrid block with three off-step points is derived using a collocation and interpolation approach. the numerical results clearly show that the developed method is able to generate good results when it is compared with the existing method in terms of error.