(Created 2010-07-25.)

NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS | FMNN10 |

**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. Problem solving 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.

- report solutions to problems and numerical results in written form.

*Judgement and approach*

For a passing grade the student must

- 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. The Poisson equation: Finite differences and the finite element method. Elliptic, parabolic and hyperbolic problems. Time dependent PDEs: Numerical schemes for the diffusion equation. Introduction to difference methods for conservation laws.

**Literature**

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

Edsberg, L: An Introduction to Modeling and Computing for Differential Equations. Wiley 2008. ISBN 0470270853, 9780470270851.