On Adaptive Multiple-Shooting Method for Stochastic Multi-Point Boundary Value Problems

Abstract

This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the corresponding solution components with a pre-specified initial approximation. Having obtained the mesh points, we solve the underlying stochastic differential equation on each shooting interval with a first-order strongly-convergent stochastic Runge-Kutta method. We illustrate the effectiveness of this approach on 1-dimentional and 2-dimentional test problems and compare our results with other non-adaptive alternative techniques proposed in the literature.