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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