Probabilistic numerical solution of wave equations with polynomial non-linearity

• المؤلف الرئيسي: Chan, Joshua Juan Yin
• مؤلفون آخرون: Nicolas Privault
• التنسيق: Final Year Project
• اللغة: English
• منشور في: Nanyang Technological University 2024
• الموضوعات: Mathematical Sciences; Partial differential equations; Wave equations; Duhamel’s solution; Monte Carlo method; Branching process; Stochastic dominance; Progeny problem
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/175826

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...