Iterative differential quadrature solutions for Bratu problem

Ola Ragb; L. F. Seddek; M. S. Matbuly

doi:10.1016/j.camwa.2017.03.033

Iterative differential quadrature solutions for Bratu problem

Ola Ragb, L. F. Seddek, M. S. Matbuly

Zagazig University

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

27 Scopus citations

Abstract

A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu's problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.

Original language	English
Pages (from-to)	249-257
Number of pages	9
Journal	Computers and Mathematics with Applications
Volume	74
Issue number	2
DOIs	https://doi.org/10.1016/j.camwa.2017.03.033
State	Published - 15 Jul 2017
Externally published	Yes

Keywords

Bratu equation
Differential quadrature
Multiple solutions
Nonlinear equations

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10.1016/j.camwa.2017.03.033

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title = "Iterative differential quadrature solutions for Bratu problem",

abstract = "A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu's problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.",

keywords = "Bratu equation, Differential quadrature, Multiple solutions, Nonlinear equations",

author = "Ola Ragb and Seddek, \{L. F.\} and Matbuly, \{M. S.\}",

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AU - Seddek, L. F.

AU - Matbuly, M. S.

PY - 2017/7/15

Y1 - 2017/7/15

N2 - A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu's problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.

AB - A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu's problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.

KW - Bratu equation

KW - Differential quadrature

KW - Multiple solutions

KW - Nonlinear equations

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SP - 249

EP - 257

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -

Iterative differential quadrature solutions for Bratu problem

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