Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems | Zendy

Grey Ballard | Zendy; John V. Baxley | Zendy; Nisrine Libbus | Zendy

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Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems

Author(s) -

Grey Ballard,

John V. Baxley,

Nisrine Libbus

Publication year - 2006

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2006.5.251

Subject(s) - shooting method , a priori and a posteriori , boundary value problem , computation , nonlinear system , invertible matrix , mathematics , singular boundary method , value (mathematics) , boundary (topology) , mathematical analysis , mathematical optimization , algorithm , boundary element method , physics , finite element method , philosophy , statistics , epistemology , quantum mechanics , pure mathematics , thermodynamics

We consider nonlinear boundary value problems with multiple solutions. A method is proposed for the computation of such solutions which depends crucially on known a priori qualitative information about the behavior of the solutions. The method is a two-stage method where the second stage is a shooting method and initial values of the shooting parameters are found in a first stage which approximates the boundary value problem with a discrete approximation. Both nonsingular and singular problems are considered.

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