Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation

Teruya Minamoto; Mitsuhiro T. Nakao

doi:10.1016/j.cam.2006.02.023

Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation

Teruya Minamoto^*, Mitsuhiro T. Nakao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

A numerical verification method to confirm the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation is presented. Using certain systems of equations corresponding to a double turning point, we derive a sufficient condition for its existence whose satisfaction can be verified computationally. We describe verification procedures and give a numerical example as a demonstration.

Original language	English
Pages (from-to)	177-185
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	202
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2006.02.023
Publication status	Published - 2007 May 15
Externally published	Yes

Keywords

Double turning point
Extended system
Fixed point theorem
Numerical computation with guaranteed accuracy
Perturbed Gelfand equation
Two-parameter dependent nonlinear problem

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Numerical Analysis

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10.1016/j.cam.2006.02.023

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abstract = "A numerical verification method to confirm the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation is presented. Using certain systems of equations corresponding to a double turning point, we derive a sufficient condition for its existence whose satisfaction can be verified computationally. We describe verification procedures and give a numerical example as a demonstration.",

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AU - Minamoto, Teruya

AU - Nakao, Mitsuhiro T.

PY - 2007/5/15

Y1 - 2007/5/15

N2 - A numerical verification method to confirm the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation is presented. Using certain systems of equations corresponding to a double turning point, we derive a sufficient condition for its existence whose satisfaction can be verified computationally. We describe verification procedures and give a numerical example as a demonstration.

AB - A numerical verification method to confirm the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation is presented. Using certain systems of equations corresponding to a double turning point, we derive a sufficient condition for its existence whose satisfaction can be verified computationally. We describe verification procedures and give a numerical example as a demonstration.

KW - Double turning point

KW - Extended system

KW - Fixed point theorem

KW - Numerical computation with guaranteed accuracy

KW - Perturbed Gelfand equation

KW - Two-parameter dependent nonlinear problem

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation

Abstract

Keywords

ASJC Scopus subject areas

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