Boundary Value Problems: Numerical Methods

This lecture covers the motivation and examples of boundary value problems, including the vertical deflection of a string and diffusion in a catalyst particle. It also provides a general description of boundary value problems, discussing the finite difference method in 1D. The lecture introduces the need for numerical methods due to the complexity of analytical solutions and the challenges posed by non-simple boundaries. It explains the discretization of the domain and the use of finite difference methods to solve boundary value problems, emphasizing the approximation of local derivatives. The Taylor series and forward/backward difference methods are also discussed for solving ODEs.