(Created 2008-07-17.)

NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS | FMN130 |

**Aim**

The aim of the course is to teach computational methods for solving ordinary and partial differential equations. This includes the construction, application and analysis of basic computational algorithms. Problemsolving by computers is a central part of the course.

*Knowledge and understanding*

For a passing grade the student must

*Skills and abilities*

For a passing grade the student must

- be able to evaluate both accuracy and relevance of numerical results

*Judgement and approach*

For a passing grade the student must

- write a logically well structured report in suitable terminology on the construction of basic mathematical models and algorithms.

- write an algorithmically well structured report in suitable terminology on the numerical solution of a mathematical problem

**Contents**

Methods for time integration: Eulers method, the trapezoidal rule. Multistep methods: Adams methods, backward differentiation formulae. Explicit and implicit Runge-Kutta methods. Error analysis, stability and convergence. Stiff problems and A-stability. Error control and adaptivity. Differential algebraic systems. The Poisson equation: Finite differences and the finite element method, multigrid. Time dependent PDEs: Numerical schemes for the diffusion equation. An introduction to finite volume schemes for conservation laws.

**Literature**

Iserles, A: Numerical analysis of differential equations. Cambridge University Press, 1996, ISBN 0-521-55655-4.

Tveito, A. and Winther, R.: Introduction to partial differential equations. A computational approach. Springer 1998, ISBN 0-387-98327-9