Intro to Num Solution of DEs
Class Demos


Jan 11-15

IVP Example Comparisons of various IVP solvers
ode.f FORTRAN code used for IVPs
Examples for solving BVPs

Jan 18-22

Convergence of finite difference methods.
Tridiagonal Solver
bvp.f FORTRAN code used for BVPs
FEM courses at RPI

Jan 25-29

Comparisons between the FEM and the FDM
Maple Worksheet illustrating solution of heat equation
Example of solution of heat equation.

Feb 1-5

Stability of implicit and explicit methods
Comparisons of implict and Crank-Nicolson methods

Feb 8-12

Surface Plots obtained from numerical solution of heat equation
Maple session used to generate surface plots
Example of data file read by Maple
FORTRAN code used to generate surface data

Feb 15-19

Comparisons between implicit and Crank-Nicolson methods
FORTRAN code used for comparisons

March 15-19

How to Make a MATLAB Movie
Square wave movie
Source MATLAB commands used to produce square wave movie.
Wave Movie 1 wave motion illustrating instability of explicit method.
Wave Movie 2 wave motion illustrating stability when CFL condition satisfied.
Source MATLAB commands used to produce wave movies coming from using explicit method
Source FORTRAN code used to generate data

March 22-26

Wave Movie 3 Comparison between explicit and implicit methods for wave equation.
Wave Movie 4 Comparison between explicit (with CFL=0.988) and explicit (with CFL=0.489)
Frames from above two movies
Phase Velocities for examples in above two movies.
wave.f FORTRAN program used to generate data for explicit method
data.m Sample data file to be used by MATLAB
waves.m MATLAB commands used to generate movie from FORTRAN data file

April 19-23

SDM outline of the steepest descent method
CGM outline of the conjugate gradient method
SDM vs CGM comparison between the SDM and the CGM.
MATLAB code used for CGM method
Iterative Solvers comparison between various interative methods to solve linear systems.
Solution of Laplace's Eq surface and contour plots of solution
FORTRAN code used to solve Laplace's equation
Maple commands to produce plots of solution from FROTRAN data file.


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