Introduction to numerical techniques in electromagnetics

With reference to Fig 8.1, corresponds to the voltage V_ij. For the five node mesh configuration of Fig 8.2, the voltages are defined as:

............................................................................... (8.3a)

.....................................................................  (8.3b)

....................................................................  (8.3c)

....................................................................  (8.3d)

....................................................................  (8.3e)

Let , , and represent the midpoint of the arms as shown in Fig 8.2. In order to replace the Poisson equation (8.2) by difference equations, we obtain the approximate first derivatives at the points to and use these first derivatives to approximate the second derivative.