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189-579B Numerical Differential Equations (4 credits) Professor: Martin J. Gander |
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Goto the course webpage
Course Description
Many
physical
phenomena can be formulated as differential equations, for example the
flow of a fluid or the temperature in your room. The solution of these
equations is however challenging and analytical methods rarely suffice
to obtain the desired results. Only numerical methods can solve the problems
of interest in applications.
This
course introduces you to the theory of modern numerical methods for solving
ordinary differential equations (ODEs) and partial differential equations
(PDEs). We use throughout the course Matlab to develop prototype
codes and we use Maple to avoid tedious hand calculations. This
is the ideal course for you if you are an engineer or applied mathematician
who needs to solve ODEs and PDEs in your application area. After the course
you will be able to make an informed choice when solving your problems
numerically.
Topics
-
Numerical methods for
ordinary
differential equations (Linear multi-step and Runge-Kutta methods, consistency,
stability and convergence, adaptive integration). - Hamiltonian problems, symplectic integration.
- Shooting methods for boundary value problems.
- Numerical methods for elliptic partial differential equations, including finite difference, finite element, finite volume and spectral methods.
- The method of lines for hyperbolic and parabolic partial differential equations, implicit and explicit time integration.
- Multi-grid methods and domain decomposition.
The main prerequisite for the course is that you understand the continuous
problems for which numerical methods are developed. So you need to know
ODEs and PDEs at the level taught in a 'methods of mathematical physics'
course and basic numerical analysis including programming.
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