A new method of determining eigenvalues and eigenfunctions
John A. T. Bye · The Computer Journal · 1967
An analytical solution of the general eigenequation [equation: see PDF] where [equation: see PDF] is independently linear in the Y(r) and λi, and Y(x) is the eigenfunction and λ is the eigenvalue, is developed. The eigenfunction is obtained as an analytic function of x, and the eigenvalue λ is the ratio between successive functions in an expansion. The solution is always convergent, and can be used as a practical method of computing eigenparameters to a high degree of precision. Two examples of computer application are given in which the solutions are obtained as power series.