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

The purpose of this work is to propose a new efficient initial guess algorithm rather than the conventional Newton method to meet the adjoint terminal conditions, rapidly. Thus, 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. The boundary value problem is formulated as a system of equations i.e. initial value problems with one unknown initial condition. The efficiency and accuracy of the Shooting method is enhanced by improving the initial guess and then solving the problem iteratively.