An iterative solution method for p-harmonic functions on finite graphs with an implementation
This was the title for my final thesis for my masters degree in Mathematics, completed in 2009. In the paper I studied a method for finding the solution to Dirichlet's boundary value problem over graphs. The method I looked at is based on the idea of stepping through all the nodes and solving the value for the node while assuming that the neighbors had the correct values. In the paper I prove that this method will always converge to the solution and look at how quickly it will do so.
Along with the paper I also wrote a Java-program that lets the user experiment with constructing graphs and finding the solution using the method. The full source for the program is included in a .tar.gz file below for those who wants to look at it. If you want to try it you can either use the java applet below or download the .jar file and run it as a stand alone program. The stand alone version allows you to save and load graphs that you construct.
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Last updated: 2019-11-29