Nonlinear Boundary-value Problems with Multiple Solutions

Shijun Liao ()
Additional contact information
Shijun Liao: Shanghai Jiao Tong University

Chapter Chapter 8 in Homotopy Analysis Method in Nonlinear Differential Equations, 2012, pp 285-314 from Springer

Abstract: Abstract In this chapter, using three different types of nonlinear boundary-value equations with multiple solutions, we verify the validity of the HAM-based Mathematica package BVPh (version 1.0) for nth-order nonlinear boundary-value equations F in a finite interval 0≤z≤a, subject to the n linear boundary conditions B, (1≤k≤n), where F is a nth-order nonlinear differential operator, F is a linear operator, γ k is a constant, respectively. Especially, the socalled multiple-solution-control parameter is introduced into initial guess in order to search for multiple solutions. We illustrate that, using the BVPh 1.0 as a tool, multiple solutions of some nonlinear boundary-value equations can be found out by means of such kind of multiple-solution-control parameter.

Keywords: Initial Guess; Multiple Solution; Homotopy Analysis Metho; Auxiliary Linear Operator; Nonlinear Differential Operator (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25132-0_8

Ordering information: This item can be ordered from
http://www.springer.com/9783642251320

DOI: 10.1007/978-3-642-25132-0_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().