Iterative algorithms for nonlinear ordinary differential eigenvalue problems

Abstract

A Newton-type iterative algorithm is developed for solving a class of nonlinear eigenvalue problems. This algorithm is based on solving an algebraic equation β(λ)=0 which is defined implicitly. We show that the β(λ) in our algorithm is analytic in the area of interest and can be evaluated by solving a block bi-diagonal system. Also the Argument Principle is employed in determining the eigenvalue distribution. Numerical results for both linear and nonlinear problems are given.