A generalized quasilinearization method for second-order nonlinear differential equations with nonlinear boundary conditions

Mohamed El-Gebeily; Donal O'Regan

doi:10.1016/j.cam.2005.05.006

A generalized quasilinearization method for second-order nonlinear differential equations with nonlinear boundary conditions

Mohamed El-Gebeily^*
, Donal O'Regan

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

21 Scopus citations

Abstract

We consider the differential equation ℓ ( u ) = F ( u ), where ℓ is a formally self-adjoint second-order differential expression and F is nonlinear, with nonlinear boundary conditions. Under appropriate assumptions on ℓ, F and the boundary conditions, existence of solutions is established using the method of lower and upper solutions. A generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

Original language	English
Pages (from-to)	270-281
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	192
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2005.05.006
State	Published - 1 Aug 2006

Bibliographical note

Funding Information:
The research of the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

Keywords

Nonlinear boundary conditions
Nonlinear ordinary differential equations
Quasilinearization method
Upper and lower solutions

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2005.05.006

Cite this

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title = "A generalized quasilinearization method for second-order nonlinear differential equations with nonlinear boundary conditions",

abstract = "We consider the differential equation ℓ ( u ) = F ( u ), where ℓ is a formally self-adjoint second-order differential expression and F is nonlinear, with nonlinear boundary conditions. Under appropriate assumptions on ℓ, F and the boundary conditions, existence of solutions is established using the method of lower and upper solutions. A generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.",

keywords = "Nonlinear boundary conditions, Nonlinear ordinary differential equations, Quasilinearization method, Upper and lower solutions",

author = "Mohamed El-Gebeily and Donal O'Regan",

note = "Funding Information: The research of the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.",

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T1 - A generalized quasilinearization method for second-order nonlinear differential equations with nonlinear boundary conditions

AU - El-Gebeily, Mohamed

AU - O'Regan, Donal

N1 - Funding Information: The research of the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

PY - 2006/8/1

Y1 - 2006/8/1

N2 - We consider the differential equation ℓ ( u ) = F ( u ), where ℓ is a formally self-adjoint second-order differential expression and F is nonlinear, with nonlinear boundary conditions. Under appropriate assumptions on ℓ, F and the boundary conditions, existence of solutions is established using the method of lower and upper solutions. A generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

AB - We consider the differential equation ℓ ( u ) = F ( u ), where ℓ is a formally self-adjoint second-order differential expression and F is nonlinear, with nonlinear boundary conditions. Under appropriate assumptions on ℓ, F and the boundary conditions, existence of solutions is established using the method of lower and upper solutions. A generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

KW - Nonlinear boundary conditions

KW - Nonlinear ordinary differential equations

KW - Quasilinearization method

KW - Upper and lower solutions

UR - https://www.scopus.com/pages/publications/33646083665

U2 - 10.1016/j.cam.2005.05.006

DO - 10.1016/j.cam.2005.05.006

M3 - Article

AN - SCOPUS:33646083665

SN - 0377-0427

VL - 192

SP - 270

EP - 281

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

A generalized quasilinearization method for second-order nonlinear differential equations with nonlinear boundary conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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