Nonlinear Eigenvalue Equations with Varying Coefficients

Shijun Liao ()
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Shijun Liao: Shanghai Jiao Tong University

Chapter Chapter 9 in Homotopy Analysis Method in Nonlinear Differential Equations, 2012, pp 315-361 from Springer

Abstract: 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 ≤z ≤a, subject to the n linear boundary conditions B (1 ≤ k ≤ n), 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 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-25132-0_9

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