Overview
During this two-week intensive summer program, I collaborated with faculty and fellow students through a combination of lectures and hands-on projects exploring partial differential equations and their numerical simulations. A program homepage along with a list of the levturers/organizers may be found here.
Project: Nonlinear Scalar PDEs & Soliton Dynamics
Our project investigated nonlinear scalar PDEs with a focus on soliton dynamics and wave behavior in dispersive systems. We analyzed various wave solutions for the Klein-Gordon and sine-Gordon equations, then implemented vectorized Python solvers with second-order accuracy to model and visualize these solutions computationally.
Lecture Topics
ODEs and time-stepping methods
PDEs, Fourier transforms, the wave equation, transport phenomena, and shocks
Conservation laws, energy and heat transfer, and gas dynamics
Finite difference methods
Finite element methods