As an example the discretized form of POISSON's equation (2.14)
will be written using the finite difference method. Assuming constant permittivity
POISSON's equation in the one-dimensional case is given by
(3.11)
The discretized representation is obtained by replacing the second order derivative by the
central difference quotient eqn. (3.10) at all inner points
(3.12)
The equations for and are determined by the boundary conditions. By rewriting
this equation in the form
(3.13)
the coefficients are found to be
(3.14)
(3.15)
The coefficient matrix resulting from the linear equation system
eqn. (3.13) is symmetric and only the diagonal and the secondary diagonal
are filled with elements different from zero.