Section 6: Solution of Partial Differential Equations (Matlab Examples).

·    Poisson (Elliptical) Equation
·    Laplace Equation
·    Diffusion (Parabolic) Equation
·    Wave (Hyperbolic) Equation
·    Boundary-Value Problem
·    Crank-Nicolson Scheme
·    Average Value Theorem
·    Simple iteration
·    Neumann Conditions
·    Off-Mesh Boundaries

Most of these algorithms can be found in Numerical methods for physics  by Alejandro L. Garcia (Englewood Cliffs, N.J : Prentice Hall, 1994. - 0131519867) and can be collected from the library (shelf number 530.15).
The below link points to the web page of the above mentioned book: http://www.wenet.net/~algarcia/nummeth/nummeth.html
Other files Matlab, C++, or Fortran implementations of numerical methods for physics can be found at: http://www.wenet.net/~algarcia/nummeth/Programs2E.html

diffusion.m  Program to solve the neutron diffusion equation  using the Forward Time Centered Space (FTCS) scheme.

fftpoisson.m Program to solve the Poisson equation using  MFT method (periodic boundary conditions).

fwave.m Program to solve the hyperbolic equtionn, e.g. wave equation.

heat1.m Program to solve the heat equation on a 1D domain [0,L] for 0 < t < T, given initial temperature profile and with boundary conditions u(0,t) = a and u(L,t) = b for 0 < t < T.

heat2.m Program to solve the parabolic eqution, e.g. heat flow equation.

schro_crank_nicholson.m Program to solve the Schrodinger equation for a free particle using the Crank-Nicolson scheme

schrot.m Program to solve the Schrodinger equation using sparce matrix Crank-Nicolson scheme (Particle-in-a-box version)

Valentin Muresan, Dublin City University, muresanv@eeng.dcu.ie