ON TWO METHODS OF SOLVING EIGEN VALUE PROBLEM FOR A SET OF SECOND-ORDER DIFFERENTIAL EQUATIONS OF THE MULTIDIMENSIONAL ANGULAR COULUMB FUNCTIONS METHOD

A. I. Golubev, V. M. Povyshev, A. A. Sadovoy, M. K. Sarayeva
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1987. Вып.2. С. 57-63.

      Two numerical methods are proposed for solving eigen/value problem for a set of second-order ordinary differential equations arising when the method of multidimensional angular Coulomb functions is used in multi-electron atom theory. In Galerkin method using all particular solution limitations the solution of lower eigen/values is reduced to nonlinear algebraic equation solution. In the Sturm distribution method a set of linear algebraic equations is solved numerically to derive eigen/values and eigen vectors. Numerical results are supplied illustrating convergence of both methods.