Numerical Solutions of 1 dimensional PDEs

This web page provide some notes on how to solve a 1-dimensional partial differential equation numerically. Its provides some lecture notes as a postscript file plus all the sources files.

The prerequisites for the notes are some programing experience with C++ and some knowledge on the numerical integration of ordinary differential equations.


Scattering of two sine-Gordon kinks.

Movies

The movies below are mng movie files that can be viewed using Mozilla or Netscape 7. Netscape 4 and windows explorer don't seem capable of displaying these movies. On Linux/Unix, the file can also be viewed using animate. Download the movie file and execute the command 

   % animate FILE.mng
Scattering of two sine-Gordon kinks. Sine-Gordon Breather. Scattering of two sine-Gordon breathers. Scattering of Kortweg-Devries solitons on a periodic grid.

Lecture Notes

Lecture notes as a postscript file

Source: difSineGordon

These are the source file of the program described in chapter 2.

Source: sineGordon

These are the source files of the program described in chapter 4. To use the program, put all the files in the same directory. Create the directory DATA in that directory and execute the commands 
  % make sineGordon
  % sineGordon sineGordon.par
The first one compiles the program and the second one runs it. All the data files are put in the directory DATA. To run the program for other parameters, just modify the file sineGordon.par and run sineGordon again.

Source: radialHeat

These are the source file of the program described in chapter 5. These files should be saved in the same directory as the sineGordon files. One can also modify the Makefile to place them in a different directory. To use the program execute the commands 
  % make radialHeat
  % radialHeat radialHeat.par
The first one compiles the program and the second one runs it. All the data files are put in the directory DATA.

Source: sineGordon_relax

These are the source files of the program described in chapter 6. To use the program, put all the files in the same directory as the sineGordon. The Makefile given here can be used to compile both program. 
  % make sineGordon
  % sineGordon sineGordon_relax.par
The first one compiles the program and the second one runs it. All the data files are put in the directory DATA. To run the program for other parameters, just modify the file sineGordon.par and run sineGordon again.
Author: b.m.a.g.piette@durham.ac.uk

Revised 27/10/04.