**By R. Belmans**

**The field domain of interest is discretised by a grid**, where the grid-lines are in parallel to the co-ordinate axes. This type of mesh is called an orthogonal grid and must not consist of equidistant grid-points (Fig. 5.23). The grid-distancescan be different.

**Fig. 5.23. Numerical discretisation for the FDM.**

**Fig. 5.24. Approximation of the potential distribution by a Taylor series.**

**The potential distribution over the studied domain is approximated by the first terms of a Taylor series (Fig. 5.24):**

**The differential equation of the particular** field problem is locally transferred into a difference equation. For example, calculating the value of a potential distribution at point 0, by using the 4-point approach (Fig. 5.23), and a grid distance d with a derivative

is expressed by a finite difference with a known approximation error T](x). By considering only the first terms of the Taylor series, this error is known and dependent on the grid distance. Forward,

backward

and central difference

are used to assemble a system of linear equations to calculate the potentials at all grid points. This leads to a large linear system of equations to be solved. The potentials at the mesh points represent the approximated field solution. To obtain an accurate field solution a fine discretisation is required.