Improving the efficiency of the multiple shooting technique (Q1205927)

The numerical solution of a boundary value problem by the multiple shooting technique is considered. In this situation Runge-Kutta methods are applied for the integration of the associated initial value problems for the variational equation together with the original ordinary differential equation. A special Runge-Kutta method, with low computational cost per step, is designed with the purpose of saving Jacobian evaluations in the integration process of the the variational equation. The adopted Runge-Kutta method is different from the one for the original ordinary differential equation. Finally, some numerical experiments are presented showing a substantial reduction in the number of Jacobian evaluations in comparison with the code in IMSL.