Solving coupled non-linear higher order BVPs using improved shooting method

Abstract

Abstract The focus of this paper is to use better algorithms for obtaining refined initial guesses with shooting method to solve the coupled boundary value problems. Boundary value problem is formulated as a system of equations i.e. initial value problems with one unknown initial conditions. The purpose of this work is to propose a new efficient initial guess algorithms rather than conventional Newton method to meet the adjoint terminal conditions, rapidly. The efficiency and accuracy of Shooting method is enhanced by improving initial guess and then solving the problem iteratively.