INVARIANT IMBEDDING AND CALCULATION OF EIGENVALUES FOR STURM-LIOUVILLE SYSTEMS

A new technique based upon an invariant imbedding-Ricatti transformation approach is presented for the calculation of eigenvalues of Sturm-Liouville type systems of differential equations. A very simple numerical procedure is developed which is easily programmed and which uses reliable subroutines. The method is capable of handling a large class of problems. Included among these are problems in which the eigenvalues appears in a non-linear fashion, cases in which the eigenvalue occurs in the boundary condition, and equations which have singularities. The numerical computations are generally well-conditioned and very accurate results were obtained. © 1969 Springer-Verlag.