Solving Nonlinear Partial Differential Equations via Deep Galerkin Method

This paper introduces a one-dimensional nonlinear Black-Scholes equation. Because nonlinear models are difficult to obtain analytical solutions, finite difference schemes are usually used to solve them. Numerical solutions of partial differential equations have always been a hot research topic in the frontier; the finite element method, finite body method, and other methods are commonly used in research. In general, these methods require the use of grids to approximate the definition space of PDEs. When we have a finer grid, the more accurate solution will be. However, the smaller the grid, the higher the computing cost and the larger the storage space. Therefore, the meshless method is adopted in this paper.