Authors’ abstract: A precise method for solving systems of coupled ordinary differential equations of second order in one variable is presented. The method consists mostly of algebraic manipulations and is very efficient on vector computers. The method is applied to the solution of the three-body Schrödinger equation. Besides giving, in contrast to variational methods, uniformly precise expectation values of operators including the Hamiltonian, the method allows one to study the analytic structure of the wave function. Applications to the He atom, the muonic helium atom, and the \(\mu \text{dt}\) molecular ion are presented. No extended precision intermediate calculations are required.