Shooting Methods for Numerical Solution of Nonlinear Stochastic Boundary-Value Problems

Abstract

In the present investigation, shooting methods are described for numerically solving nonlinear stochastic boundary-value problems. These stochastic shooting methods are analogous to standard shooting methods for numerical solution of ordinary deterministic boundary-value problems. It is shown that the shooting methods provide accurate approximations. An error analysis is performed and computational simulations are described.

Keywords:

• Broyden's method
• Itô and Stratonovich stochastic differential equations
• Nonlinear stochastic boundary-value problems
• Shooting methods

Mathematics Subject Classification:

• 60H35
• 65C30
• 60H10

Acknowledgments

The author is grateful to Edward J. Allen for many helpful discussions.