Discretization of Coupled Wave Equations

The coupled wave equations are discretized using implicit finite difference method in the temporal domain and backward difference method in the spatial domain, facilitating numerical simulation of stimulated Brillouin scattering's energy reflectivity and SBS threshold energy. In practice, computational accuracy can be improved by increasing temporal steps while spatial resolution is enhanced through additional grid nodes. The algorithm typically involves: 1. Discretizing partial differential terms using central/backward difference operators 2. Assembling coefficient matrices for linear systems 3. Implementing iterative solvers (e.g., Gauss-Seidel or conjugate gradient methods) Further optimization can be achieved by incorporating advanced models including nonlinear refractive indices and device structures, which may require additional physical parameters and boundary condition handling in the code. These enhancements allow deeper investigation of practical application impacts through parameterized simulations.