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Nonlinear Eigenvalue Equations with Varying Coefficients

  • Shijun Liao

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 in a finite interval 0 ≤za, subject to the n linear boundary conditions B (1 ≤ kn), where F denotes a nth-order nonlinear ordinary differential operator, ℐ is a linear differential operator, B is a constant, u(z) and α 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.

Keywords

Initial Guess Multiple Solution Homotopy Analysis Method Nonlinear Eigenvalue Problem Linear Boundary Condition 
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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shijun Liao
    • 1
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina

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