Numerical Methods for Ordinary and Partial Differential Equations

Course content

The students master the use of numerical methods for the solution of ordinary and partial differential equations, and they are able to interpret the numerical results. They know one-step and multi-step methods and the concept of step-size control. They understand the particular properties of stiff systems. The students know the methods of finite elements and of finite differences and respective adaptive procedures. They have experienced with software implementations.

Content
Euler method, Euler-Heun method, Runge-Kutta method, Butcher scheme, consistency and convergence, consistency order, step size control , Adams-Bashforth, Adams-Moulton, BDF- formulas, implicite schemes, A-stabilty, finite differences, finite elements, mesh generation, adaptive mesh refinements