Local Discontinuous Galerkin Method for Nonlinear BSPDEs of Neumann Boundary Conditions with Deep Backward Dynamic Programming Time-Marching
Abstract
This paper aims to present a local discontinuous Galerkin (LDG) method for solving nonlinear backward stochastic partial differential equations (BSPDEs) with Neumann boundary conditions. We establish the $L^2$-stability and optimal error estimates of the proposed numerical scheme. Two numerical examples are provided to demonstrate the performance of the LDG method, where we incorporate a deep learning algorithm to address the challenge of the curse of dimensionality in backward stochastic differential equations (BSDEs). The results show the effectiveness and accuracy of the LDG method in tackling BSPDEs with Neumann boundary conditions.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Stochastic processes and financial applications
Numerical methods for differential equations
Publication details
- Journal / source
- Communications in Computational Physics
- Volume
- 39
- Issue
- 4
- Pages
- 1299–1331
- Publication date
- 18 January 2026
- Language
- EN