Successive Overrelaxation for Elliptic PDEs

Consider Laplace s equation in two dimensions (this is an elliptic equation)  

This equation represents many steady-state phenomena in two dimensions, such as temperature distributions, laminar flow distributions, and voltage distributions. 

Substituting second-order correct finite difference analogs into Equation 8.23, there results 

FIGURE 8.3 Nomenclature finite difference representation of heat transfer in a flat plate. 

If Ax = Ay, this can be written as the average of the four surrounding temperatures as in Equation 8.26. 

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