Improved Implementation of Multiple Shooting for BVPs

Boundary value problems arise in many applications, and shooting methods are one approach to approximate the solution of such problems. A Shooting method transforms a boundary value problem into a sequence of initial value problems, and takes the advantage of the speed and adaptivity of initial value problem solvers. The implementation of continuous Runge-Kutta methods with defect control for initial value problems gives efficient and reliable solutions. In this paper, we design and implement a boundary value solver that is based on a shooting method using a continuous Runge-Kutta method to solve the associated initial value problems. Numerical tests on a selection of problems show that this approach achieves better performance than another widely used existing shooting method.