| Recommended semester: 4th -7th semester |
| Scope and form: Lectures and project work in data bar. |
| Evaluation: Approval of coursework/reports
|
| Examination: 13-scale |
| Previous course: 04202 + 04211 |
| Prerequisites: Basic numerical analysis (e.g. 02601) and knowledge of complex variables with applications (e.g. 02643). |
| Participant limitation: Max. 50 |
| Aim: To give the students the ability to analyse both ordinary and partial differential equations resulting from problems in physics and engineering, and to give them an understanding of the basic numerical methods used to solve these problems via hands on experience. |
Contents: The course begins with a short review of analytic solutions to differential equations via the calculus of variations, Fourier and Laplace transform, and the method of characteristics. Thereafter, the emphasis is on numerical analysis and solution techniques.
Ordinary differential equations: Numerical methods for solving initial-value problems; one-step and multi-step methods; the concepts of accuracy, convergence, order and stability; stiff sytems; simuation methods that run in real time; systems with shocks or phase-shifts; boundary-value problems and the shooting method.
Partial differential equations: General classification; the method of lines; the finite-difference method, including analysis of stability and convergence, and it's application to several key problems; iterative methods for solving large systems of equations; introduction to the finite-volume, the finite-element, and the spectral method.
Along with the theory, the course addresses many issues concerned with the practical design and implementation of efficient computational tools; with report topics which are taken from real-world applications. Although the reports may be completed using any programming language, use of Matlab is recommended and some experience with the language will be an advantage. |
| Contact: Per Grove Thomsen, building 305, (+45) 4525 3073, pgt@imm.dtu.dk |
| Department: 002 Informatics and Mathematical Modelling |
| Course URL: http://www.imm.dtu.dk/courses/02685 |
| Keywords: ordinary differential equations, partial differential equations, numerical methods, sparse matrices |
| Updated: 17-04-2001 |
