this link may be help you
https://www.mathworks.com/matlabcentral/answers/286133-2d-crank-nicolson-adi-scheme
https://matlabgeeks.weebly.com/uploads/8/0/4/8/8048228/crank-example_with_matlab_code__doc_.pdf
https://www.researchgate.net/post/How_to_write_Matlab_code_for_Implicit_2D_heat_conduction_using_Crank_Nicolson_method
https://www.mathworks.com/matlabcentral/fileexchange/45542-heat-equation-2d-t-x-by-implicit-method?s_tid=mwa_osa_a
Dear Abbas Miry and Ömer Şayli
The codes provided in your links are for 1-D problems. Do you have any examples of applications for the multidimensional problems?
In particular, I have not coded but these are some additional resources (1-a and 1-b may attract your attention more I think, from http://www-udc.ig.utexas.edu/external/becker/)
1-a)http://www-udc.ig.utexas.edu/external/becker/Geodynamics557.pdf
1-b) http://www-udc.ig.utexas.edu/external/becker/teaching/557/matlab_code/all.tgz
2) https://math.stackexchange.com/questions/3177783/implementing-numerical-scheme-for-2d-heat-equation-in-matlab/3180821
3) (Python) https://pycav.readthedocs.io/en/latest/api/pde/crank_nicolson.html
4) (python) Chapter Diffusion Equations
5) http://geodynamics.usc.edu/~becker/teaching/557/problem_sets/problem_set_fd_2dheat.pdf
6) http://geodynamics.usc.edu/~becker/teaching/557/matlab_code/
7-a) https://www.mathworks.com/matlabcentral/fileexchange/55058-2d-heat-equation-using-finite-difference-method-with-steady-state-solution
7-b) https://drive.google.com/file/d/0BwE9qaLqIPqSQ1lDTXF6Ry1WT28/view
It may be useful to note that the MATLAB native (stiff) solver ode23tb implements the second order TR-BDF2 method, which is increasingly acknowledged to be superior to Crank-Nicolson for many applications, while having a similar level of complexity and computational cost. The method is fully described in
Hosea, M. E., and L. F. Shampine. "Analysis and implementation of TR-BDF2." Applied Numerical Mathematics 20.1-2 (1996): 21-37.
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