I am looking for matlab code for finite difference method (hyperbolic, parabolic and elliptical).
You may want to check out this lecture series:
http://emlab.utep.edu/ee5390cem.htm
If you are interested in finite-difference time-domain, see this series:
http://emlab.utep.edu/ee5390fdtd.htm
Hope this helps!!
I propose you to study the computational book which has been written by C.A.J Fletcher titled "Computational techniques for fluid dynamics ". You can find solution of diffusion equation in 1D, 2D and 3D In this book . There is also solution of Steady state equations, convection, transfer, burger and etc and available fortarn codes in the book. Finally, Solution of Navir-Stokes for incompressible flow is comprehensively expressed in 2 methods including vorticity stream function and primitive variables. I also suggest you "Computational Fluid Dynamics" by Klaus A. Hoffman which is so similar to Feletcher's book. For a more efficient solution you can use Hybrid methods, i.e. combine Boundary Integral Equations with FDM. It is really simple and also reduce the time wasting during the numerical solution. In this regard, you can study the paper written by Professor P.Ghadimi and Dr. A. Dashtimanesh titled "Solution of 2D Navier–Stokes equation by coupled finite difference-dual reciprocity boundary element method".
Good Luck.
See the book "Numerical Solutions of Partial Differential Equations" by G D Smith, Oxford University Press London.
The "Numerical Recipes" contain not only mathematical background to numerical algorithms but also code to run them. There is a MATLAB interface to the routines available on their web site. http://www.nr.com/
"Computational Fluid Dynamics: The Basics with Application" by John D. Anderson.
This is a very very 'user friendly' book and he is a great writer.
"Numerical Methods Using Matlab", J.H. Mathews, K.D. Fink., Interantional Edition, 4th ed.
Chapters 9.9, 10.1, 10.2, 10.3 match your request perfectly.
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