THE SHOOTING METHOD: AN EFFECTIVE TOOL FOR BOUNDARY VALUE PROBLEMS IN ODE

Abstract

The shooting method is a numerical approach used to solve boundary value problems (BVPs) for ordinary differential equations (ODEs). It works by converting a BVP into an initial value problem (IVP), allowing the use of established IVP solvers like the Euler or Runge-Kutta method to iteratively find solutions. The process will begin with an initial guess for the derivative at one boundary, followed by solving the IVP and adjusting the guess based on how the computed solution aligns with the desired boundary condition at the other end. This research project discussed the theoretical foundations, practical implementation, and convergence characteristics of the shooting method, emphasizing its advantages and limitations relative to other numerical techniques. Through illustrative examples using MATLAB programing scripts, we showcased the method\u27s effectiveness in tackling complex BVPs, highlighting its importance in computational mathematics