Staff Members - Benha University
A new approach for a class of nonlinear boundary value problems with multiple Solutions
Journal of the Association of Arab Universities for Basic and Applied Sciences • 2015
Publication Information
Authors
Mourad S. Semary; Hany N. Hassan
Keywords
Variational iteration method;
Multiple solutions;
Auxiliary parameter;
h-Curve;
Nonlinear boundary value
problems
Journal
Journal of the Association of Arab Universities for Basic and Applied Sciences
Publisher
Not Available
Volume
17
Issue
Not Available
Pages
27-35
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
In this paper, an approach based on the variational iteration method (VIM) is proposed
with an auxiliary parameter to predict the multiplicity of the solutions of homogeneous nonlinear
ordinary differential equations with boundary conditions. The proposed approach is capable to pre-
dict and calculate all branches of the solutions simultaneously. Four practical problems are chosen
to show the efficiency and importance of the proposed method. The proposed approach successfully
detects multiple solutions to Bratu’s problem, the model of mixed convection flows in a vertical
channel, the nonlinear model of diffusion and reaction in porous catalysts and the nonlinear reac-
tive transport model.
with an auxiliary parameter to predict the multiplicity of the solutions of homogeneous nonlinear
ordinary differential equations with boundary conditions. The proposed approach is capable to pre-
dict and calculate all branches of the solutions simultaneously. Four practical problems are chosen
to show the efficiency and importance of the proposed method. The proposed approach successfully
detects multiple solutions to Bratu’s problem, the model of mixed convection flows in a vertical
channel, the nonlinear model of diffusion and reaction in porous catalysts and the nonlinear reac-
tive transport model.