Probabilistic numerical solution of wave equations with polynomial non-linearity

• Main Author: Chan, Joshua Juan Yin
• Other Authors: Nicolas Privault
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Mathematical Sciences; Partial differential equations; Wave equations; Duhamel’s solution; Monte Carlo method; Branching process; Stochastic dominance; Progeny problem
• Online Access: https://hdl.handle.net/10356/175826
• Institution: Nanyang Technological University

We propose a Monte Carlo solution to the wave equations with polynomial non-linearity. Writing the probabilistic representation of the Monte Carlo solution, we are able to show its expected value retrieves the Duhamel’s solution of the wave equation. Based on a stochastically dominating branching...