On Adaptive Multiple-Shooting Method for Stochastic Multi-Point Boundary Value Problems
This work addresses the challenge of solving stochastic boundary value problems, a niche area, with an incremental improvement in mesh selection.
The paper proposes an adaptive multiple-shooting method for stochastic multi-point boundary value problems, using a heuristic to select shooting points and a first-order stochastic Runge-Kutta method. The approach is demonstrated on 1D and 2D test problems, showing effectiveness compared to non-adaptive alternatives.
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.