Symbolic
generating of system equations for 2D
regular
grid for solving
difference
method
By Nasser M. Abbasi
Math 228A, UC Davis, Fall 2010
Introduction
When solving the above equation using finite difference method on square, in order to make it easy to see the internal structure of the A matrix using the standard 5 points Laplacian scheme, the following is a small function which generates the symbolic format of these equations for a given N, the number of grid points on one edge. At the end of this note, the system equations are generated for N=4,5,6,7,8. One can see the form of the A matrix with the dominant diagonal and the corresponding bands. It is mostly a sparse matrix.