Numerical Solution of Partial Differential Equations:

Numerical Solution of Partial Differential Equations: Numerical Solution of Partial Differential Equations:

Finite-Difference Methods

ESAM 446-1

Fall 2000

Hermann Riecke

In this class finite-difference methods will be discussed for the solution of partial differential equations. The class will
· present theoretical issues like convergence and accuracy of schemes, and it will
· give the students thorough experience with the numerical methods through projects in which the methods are implemented for various partial differential equations.

For the programming students can use FORTRAN, C and/or MATLAB. The latter is particularly useful for rapid prototyping. A brief introduction to MATLAB will be given and sample programs (in FORTRAN and MATLAB) will be provided.

Figure 1: Sequence of graphs (time increasing upwards) showing the scattering and dispersion of a left-traveling wave pulse (red and black) in a medium with a jump in density (green) and an inhomogeneity in the wavespeed (blue).

Technical topics to be discussed will include:
Classification and some properties of PDEs, difference approximations of derivatives in space and time, temporal errors, stability and convergence of difference approximations, initial-boundary-value problems, two-dimensional problems, operator splitting.

Time and Place: MW 11:00-12:30 TCH M152

Do you have any questions?

Phone: 491-8316, e-mail: h-riecke@nwu.edu, office: M458

File translated from T_EX by T_TH, version 1.96.
On 14 Sep 2000, 21:40.