A New Algorithm for Finding Positive Eigenvectors for a Class of Nonlinear Operators Associated with M-matrices
In this paper we state the sufficient conditions for the existence and uniqueness of positive eigenvectors for a class of nonlinear operators associated with M-matrices. We also show how to construct a convergent iterative process for finding these eigenvectors. The details of numerical implementation of this algorithm for some spectral methods of discretization of elliptic partial differential equations are also discussed. Some results of numerical experiments for the Gross-Pitaevskii Equation with non-separable potentials in a rectangular domain are given in the end of the paper.
Mathematics Subject Classification (2000)47J10
KeywordsPositive eigenvectors Nonlinear operators M-matrices Monotone fixed point theorem Gross-Pitaevskii equation
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