250023 VO Numerische Methoden für gewöhnliche und partielle Differentialgleichungen (2024S)

This course will focus on the design, analysis, implementation, and applications of numerical methods for ordinary and partial differential equations. The following topics will be covered: one-step methods for approximating ordinary differential equations (explicit and implicit Euler and Runge-Kutta methods); shooting method, finite difference and finite element methods for elliptic boundary-value problems in one spatial dimension; approximation of parabolic initial-boundary-value problems in one spatial dimension (finite element method in space, theta method in time). Other topics may include: linear multistep methods for ordinary differential equation, finite difference and finite element approximation of advection-diffusion problems and transport problems.