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

TL;DR

This paper introduces an adaptive multiple-shooting approach for solving stochastic multi-point boundary value problems, utilizing a heuristic based on drift and diffusion effects, and demonstrates its effectiveness through numerical experiments.

Contribution

The paper proposes a novel adaptive multiple-shooting method with a heuristic for selecting shooting points tailored for stochastic boundary value problems.

Findings

Effective in 1D and 2D test problems

Outperforms non-adaptive methods in accuracy

Uses stochastic Runge-Kutta for solution intervals

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.