Discretization and Solution of the SCF equations

These equations are fulfilled at every grid point Sjt and may be abbreviated as 

The application of a finite-difference method transforms the first derivatives V[u L)k point Sk into a linear combination of function values y(u L),m at contiguous points Sm around s. This yields two linear difference equations for every inner grid point s. The resulting set of linear equations can be combined into a 2m X 2m matrix equation 

Transformed solution functions y = ym = occur for point-like nu- 

For one of the coupled pair of self-consistent-field equations we may write the matrix A and the inhomogeneity vector g with the following definition of matrix and vector elements 

Those elements marked by an asterisk require additional corrections to conserve the numerical accuracy. In the first line a nonvanishing contribution from the origin has been incorporated into the elements of A by setting dl = di + Ad and e = + Ae if k, = 1 (for both equations of the cou- 

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