Dr. Mario Helm
Institut für Numerische Mathematik und Optimierung Fakultät für Mathematik und Informatik
Numerical Analysis of Differential Equations
4. BGIP, 2. CMS, 2. CSE
Summer Semester 2015
Organizational Matters and Objectives
Coordinates Lectures (2 SWS):
Dr. Mario Helm,
Phone number:∼3199,
Mail: mario.helm@math.tu-freiberg.de, Office: Nonnengasse 22 / DG 06,
Office hours by arrangement (please write an e-mail) Problem Sessions (1 SWS):
Dipl.-Math. Steffen Pacholak Phone number:∼3471,
Mail: steffen.pacholak@mailserver.tu-freiberg.de, Office: Nonnengasse 22 / DG 11.
Problem sessions offered in English and German, alternating weekly.
Qualification objectives Students shall
understand basic concepts of numerics as discretization and linearization,
be able to choose an apply appropriate numerical methods for the solution of mathematical problems arising in nature sciences and engineering,
have basic knowledge about the implementation of algorithms.
Contents
Fundamental techniques and aspects for/in the numerical solution of ordinary and partial differential equations, more precisely:
for ODEs: Euler methods, Runge Rutta Methods, Linear Multistep Methods, Stability, Stiffness;
for PDEs: Finite Difference techniques, time stepping, von Neumann stability analysis.
Workload
The overall workload of the (second part of the) module is 90 hours, according to 3 ECTS credit points. 45 hours are reserved for private studies.
Exam
Written exam (120 minutes) in English or German (you have choice),
A calculator and a formulary, as well as six hand written A4 pages (3 sheets), are permitted,
Expected date for examination: August 21, 9 a.m., please check for actuality at the end of semester!
Literature
Josef Stoer, Roland Bulirsch:Introduction to Numerical Analysis. Springer, New York 1993, second ed.
Lloyd N. Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations. Unpublished manuscript, 1996, available at
http://people.maths.ox.ac.uk/trefethen/pdetext.html
Randall J. Leveque: Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM, 2007
Arieh Iserles: A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press, 1996 K. W. Morton, David F. Mayers:Numerical Solution of Partial Differential Equations. Cambridge University Press, 1994
Acknowledgement
I would like to thank Michael Eiermann, Oliver Ernst and Feiyan Wang, who have basically contributed to this course and are authors of many of the following slides for their friendly support.
But now, let’s start the mathematical journey. We are beginning in the old harbor of Trieste. . .
