An improved shooting technique for solving boundary value problems using higher order initial approximation algorithms

Abstract

This paper introduces the better algorithms to obtain refined initial guesses with shooting method for solving boundary value problems (BVPs). Each boundary value problem (BVP) is reformulated as a system of equations i.e. initial value problems (IVPs) with one unknown initial conditions. Afterwards, the system of equations is solved using newly developed shooting method [2]. This article proposes efficient initial guess algorithms rather than conventional Newton method to approach the adjoint terminal conditions rapidly. We enhanced the efficiency and accuracy of shooting method by first improving our initial guess and then solving the problem iteratively. The suggested technique is applied to solve different nonlinear higher order boundary value problems. The results indicate that the proposed method is more efficient and accurate as compared to build-in-functions which is being used in MATLAB.