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

This paper introduces the better algorithms to obtain refinedinitial guesses with shooting method for solving boundary value problems(BVPs). Each boundary value problem (BVP) is reformulated as a systemof equations i.e. initial value problems (IVPs) with one unknown initialconditions. Afterwards, the system of equations is solved using newly de-veloped shooting method [2]. This article proposes efficient initial guessalgorithms rather than conventional Newton method to approach the ad-joint terminal conditions rapidly. We enhanced the efficiency and accuracyof shooting method by first improving our initial guess and then solvingthe problem iteratively. The suggested technique is applied to solve differ-ent nonlinear higher order boundary value problems. The results indicatethat the proposed method is more efficient and accurate as compared tobuild-in-functions which is being used in MATLAB