Invariant Imbedding Applied to Eigenvalue Problems in Mechanics

Abstract

A formal method is presented for obtaining eigenvalues of ordinary differential equations associated with problems of buckling and vibration. The method utilizes the idea of invariant imbedding which has previously been applied to two point boundary value problems in transport theory and wave propagation. The present method reduces the eigenvalue problem to an initial value problem for a matrix of Riccati equations. The numerical solution of such formulations has proved to be generally more efficient than known methods.