A numerical method for multipoint boundary value problems with application to a restricted three body problem

Abstract

A type of parallel shooting method is proposed for the solution of nonlinear multipoint boundary value problems. It extends the usual quasilinearization method and a previous shooting method developed for such problems, and reduces to usual multiple shooting techniques for two point boundary value problems. The effectiveness of the method for stiff problems is illustrated by an application to the problem of finding periodic solutions of a restricted three body problem with given Jacobian constant and unknown period.

Keywords:

• Nonlinear multipoint boundary value problem
• quasilinearization
• initial value adjusting method
• adjusting matrix
• perturbation parameter
• quadratic convergence
• restricted three body problem
• jacobian constant

C.R. Categories:

• 5.17
• 5.15

†On leave from Department of Mathematics, University of Saskatchewan, Saskatoon,Canada, S7N 0W0.

†On leave from Department of Mathematics, University of Saskatchewan, Saskatoon,Canada, S7N 0W0.

Notes

†On leave from Department of Mathematics, University of Saskatchewan, Saskatoon,Canada, S7N 0W0.