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Numerical Analysis in Mechanics
The relaxation method for the Poisson equation [Jack, §1.13]
For the origin of the method, the formula for Jacobian iteration or the formula for Gauss-Seidel iteration, read
http://www.mpi-hd.mpg.de/astrophysik/HEA/internal/Numerical_Recipes/f19-5.pdf
As for how to put the solution in matrix form Mx = b, read section 4.1 of the following webpage:
http://www.ieeeaps.org/pdfs/FA_Numerical_Poisson_Nagel.pdf
Finite element methods (Using shape functions to solve Poisson equations in two dimensions) [Jack, §2.12]: read
http://www.egyankosh.ac.in/bitstream/123456789/32845/1/Unit12.pdf
