Shooting Methods for Numerical Solution of Stochastic Boundary-Value Problems

Abstract

Abstract In the present investigation, numerical methods are developed for approximate solution of stochastic boundary-value problems. In particular, shooting methods are examined for numerically solving systems of Stratonovich boundary-value problems. It is proved that these methods accurately approximate the solutions of stochastic boundary-value problems. An error analysis of these methods is performed. Computational simulations are given. Key Words: Shooting methodsNumerical solutionsStochastic boundary-value problemsIto and Stratonovich stochastic differential equationsMathematics Subject Classification: 65C30; 60H10 Acknowledgments The research was supported by the Texas Advanced Research Program Grant ARP 0212-44-1582 and the National Science Foundation Grant DMS-0201105.