Calculation of the eigenvalue of a differential equation under non-linear parameter-dependence of its coefficients

The work deals with the eigenvalue problem of ordinary differential equatio ns with non-linear dependence of the equation coefficients on the parameter . A set of theorems for the eigenvalue estimators is presented, on the basi s of which a new algorithm can be proposed for determining the first eigenv alue of a finite-difference equation. The algorithm is demonstrated on exam ples serving as benchmark problems. Copyright (C) 1999 John Wiley & Sons, L td.