Improving the efficiency of the multiple shooting technique

AbstractIn this paper, we consider the numerical solution of a boundary value problem (BVP) by the multiple shooting technique, using Runge-Kutta (RK) methods for the integration of the associated initial value problems (IVP). A special RK method, with minimum computational cost per step, is designed with the purpose of saving Jacobian evaluations in the integration of the variational equation. Finally, some numerical experiments are presented showing a substantial reduction in the number of Jacobian evaluations