ON SOME TECHNIQUES FOR SOLVING THE PROBLEM OF AN ORDINARY DIFFERENTIAL EQUATION SYSTEM EIGENVALUES IN MACF-METHOD

V. M. Povyshev, A. A. Sadovoi
VANT. Ser. Mat. Mod. Fiz. Proc 1998. Вып.2. С. 41-44.

      Four techniques for solving the problem of eigenvalues of an ordinary differential equation system of the second order occuring during the calculation of multi-electron atom and ion properties using multi-dimensional angular Coulomb function method (MACF-method) are discussed in the paper. The comparison is made between Galerkin technique, the technique of Sturm representation of green function, the technique of Sturm representation with chosen asymptotic behaviours, and the technique with approximated asymptotics accounting which provides basic function orthogonality. Practical convergency of the last technique for a sufficiently large equation system is demonstrated.