Shooting Method for the Solution of Nonlinear Boundary Value Problems

Abstract

This work describes the shooting method for the solution of a second-order nonlinear Boundary Value Problem (BVP). This method works by first transforming each BVP into a system of Initial Value Problems (IVPs). The initial conditions associated with the IVPs are then adjusted to match the boundary conditions associated with the BVPs by making guesses or “shooting for values”. This process is repeated using the secant method to determine the right value until the initial conditions are satisfactorily closed to the boundary conditions. The IVPs are solved using the Euler method. The Euler method was chosen for this work primarily due to its simplicity and ease of implementation. An illustrative example is considered and the results obtained show the importance of the shooting method to BVPs.