Numerical Methods for Boundary Value Problems

This lecture covers the numerical methods for solving boundary value problems (BVPs) using finite difference methods, fast Fourier transforms, and finite element methods. It explains the general description of BVPs, transfer problems, and the finite difference method strategy. The lecture also delves into solving BVPs in 1D using discretization, translating boundary values into equations, and employing the Finite difference time domain solutions for non-steady state systems. Additionally, it explores spectral methods using FFT to approximate derivatives and solve partial differential equations (PDEs) with spectral methods. The lecture concludes with practical examples and applications of these numerical methods.