Numerical Methods for ODEs (PhD)UNIVERSITÀ DELLA SVIZZERA ITALIANA
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- Mendrisio (Svizzera)
Ordinary differential equations (ODEs) and initial value problems (IVP) are ubiquitous in almost all applications arising in computational science. The course will start out with some basic concepts from ODE theory and then continue with the discussion of different explicit and implicit one-step. Performance of different methods for different types of problems will be investigated numerically and the observed behaviour will be explained by mathematical analysis. This will lead to important theoretical concepts like consistency, stability and convergence. In applications, one often wants to employ procedures that automatically refine time-steps in regions where the error is large: Approaches to adaptive step-size control will be discussed and tested. Because IVPs often stem from the semi-discretization of PDEs, in the final part of the course some examples will be analyzed of how spatial and temporal discretization can interact, particularly in problems with wave-like solutions.