New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems

This paper is devoted to introducing a novel numerical approach for approximating solutions to Boundary Value Problems (BVPs). Such an approach will be carried out by using a new version of the shooting method, which would convert the BVP into a linear system of two initial value problems. This system can then be solved by the so-called Obreschkoff approach. The numerical solution of the main BVP will ultimately be a linear combination of the solutions of the two system of equations. Two physical applications will be presented in order to confirm that the suggested numerical technique is valid.