Introduction to numerical techniques in electromagnetics

Further, for Laplace equation, and equation (8.8) simplifies to

.....................................................(8.9)

Thus we see that voltage at the central node is the mean of the voltages at the other four nodes.

With reference to Fig 8.1, equation (8.8) can be written as

....................(8.10)

Equation (8.8) & equation (8.9) can be used to solve Poisson's and Laplace's equation respectively when uniform grids are used. These equations, along with the specified boundary conditions can be used to solve a given problem in two ways, the same is illustrated with the help of an example.