Nonlinear Eigenvalue Equations with Varying Coefficients

Abstract

Five different types of examples are used to illustrate the validity of the HAM-based Mathematica package BVPh (version 1.0) for nonlinear eigenvalue equations F [z [ [ , u, λ ] = 0 in a finite interval 0 z a, subject to the n linear boundary conditions B k [z [ [ , u] = γ k γ γ (1 k n), where F denotes a nth-order nonlinear ordinary differential operator, B k is a linear differential operator, γ k γ is a constant, u(z) and λ denote eigenfunction and eigenvalue, respectively. These examples verify that, using the BVPh 1.0, multiple solutions of some highly nonlinear eigenvalue equations with singularity and/or multipoint boundary conditions can be found by means of different initial guesses and different types of base functions.