Course - Numerical Solution of Differential Equations by Difference Methods - TMA4212
Numerical Solution of Differential Equations by Difference Methods
About
About the course
Course content
Difference schemes for different types of partial differential equations. Analysis of consistency, order, stability and convergence. Solution of linear systems by iterative methods and preconditioning. Finite element method.
Learning outcome
1. Knowledge. The student understands the basic theory underlying the numerical solution of partial differential equations. The student masters error analysis of difference methods, and understands the concepts consistency, stability and convergence. The student has a basic understanding of the finite element method and iterative solution techniques for systems of equations.
2. Skills. The student is able to choose suitable methods for elliptic, parabolic and hyperbolic partial differential equations. The student is able to set up, implement and analyze discretization methods for selected partial differential equations. The student is able to design numerical experiments serving the purpose to verify if a PDE-solver is implemented correctly. The student is able to choose and apply suitable iterative methods for equation solving.
3. General competence. The student masters written and oral presentation of scientific problems and of the results obtained in the project work. The student is able to apply aquired mathematical knowledge in linear algebra and calculus to achieve the other goals of the course.
Learning methods and activities
Lectures, project and exercises.
Further on evaluation
In order to pass the course, a passing grade (A-E) in the written exam is required.
The portfolio consists of one project work. A more detailed descripttion of the form of the project presentation will be published on the webpage of the course at the start of the semester.
The re-sit examination for the written exam may be given as an oral examination. The re-sit exam is in August. There will be no re-sit examination for the portfolio. Students are free to choose Norwegian or English for written assessments or the portfolio.
Recommended previous knowledge
TMA4215 Numerical Mathematics or similar.
Course materials
Will be announced at the start of the course.
Subject areas
- Mathematics
- Technological subjects