Numerical-differentiation approach for the ground state of the He atom

Abstract
The method of numerical differentiation is applied to solve the coupled set of ordinary differential equations for a three-body system derived in the previous paper. This is done for the ground state of the He atom. The matching of the forward and backward numerical solutions of the coupled system of differential equations is achieved by repeated applications of Newton's correction method. The matching of up to 16 coupled curves is carried out successfully, but the results obtained show that a very large number of coupled terms are required to obtain a good convergence of the ground-state energy.