Inhalt
Kommentar |
Many problems in science and engineering are modelled by partial differential equations (PDEs). Three basic types of PDEs appear: elliptic equations, parabolic equations and hyperbolic equations. In this lecture, we introduce numerical methods for the solution of each problem type. For example, finite difference schemes and finite element methods are applied. As in numerical methods for ordinary differential equations, we investigate consistency, stability and convergence of the techniques. The usage of modern software packages is considered. Examples for PDEs, which are discussed in the lecture, are: elliptic type: Laplace eq., Poisson eq. (static problems); parabolic type: heat eq. (diffusion processes); hyperbolic type: wave eq. (transport processes).
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Literatur |
Main document: Script by Prof Roland Pulch (Univ. Greifswald) and Dr. E. Jan W. ter Maten (Bergische Univ. Wuppertal) 2020: Numerical Analysis and Simulation of Partial Differential Equations (ca 250p). The script will be made available for download.
Some extra notes will be made available during the lecture series. |
Voraussetzungen |
Numerical Solution of ODEs
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Zielgruppe |
Master resp. Hauptstudium Mathematik, Master CSiS und IT, Modul Vert.NumAna |