Development of the hybrid method to solve boundary values problems in Ordinary Differential equations

Abstract The purpose of this research is the development of a Hybrid Technique for solving Boundary Value Problems (BVPs) linear & non-linear in Ordinary Differential Equations (ODEs). We display the hybrid method by using backward integration. In addition, we study the application of the hybrid method for solving BVPs with derivative boundary conditions. We used the hybrid method for solving BVPs from order third and fourth. And we ended discussion the results of the hybrid method by: 1 Increasing the number of estimations for the unknown boundary condition. 2 -Decreasing the step size of the integration. 3 -Using accurate interpolation formulae. 4 -Using higher order integration methods. Finally, we studied the stability and error control of the hybrid method.