2015
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2
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77
Some new exact traveling wave solutions one dimensional modified complex Ginzburg Landau equation
2
2
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the onedimensional modified complex GinzburgLandau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended Fexpansion method. By using homogeneous balance principle and the extended Fexpansion, more periodic wave solutions expressed by jacobi elliptic functions for the 1D MCGL equation are derived. Homogeneous method is a powerful method, it can be used to construct a large families of exact solutions to different nonlinear differential equations that does not involve independent variables.
1

70
86


Mina
Mortazavi
Department of Applied Mathematics,
School of Mathematical Sciences,
Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Applied Mathematics,
School
I. R. Iran
m_mortazavi95@yahoo.com


Mohammad
Mirzazadeh
Department of Mathematics,
Faculty of Mathematical Sciences,
University of Guilan, Rasht, Iran
Department of Mathematics,
Faculty of Mathematical
I. R. Iran
mirzazadehs2@guilan.ac.ir
Exact traveling wave Solutions
Modified Complex GinzburgLandau equation
$(G'/G)$expanson method
Homogeneous balance method
Eextended Fexpansion method
Optimization with the timedependent NavierStokes equations as constraints
2
2
In this paper, optimal distributed control of the timedependent NavierStokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasiNewton algorithm, a novel calculation of the gradients and an inhomogeneous NavierStokes solver, to find the optimal control of the NavierStokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.
1

87
98


Mitra
Vizheh
Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151159, Iran
Department of Mathematics, Shahed University,
I. R. Iran
mitravizheh@gmail.com


Syaed Hodjatollah
MomeniMasuleh
Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151159, Iran
Department of Mathematics, Shahed University,
I. R. Iran
momeni@shahed.ac.ir


Alaeddin
Malek
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: 14115134, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
mala@modares.ac.ir
Optimal Control Problems
NavierStokes equations
PDEconstrained optimization
quasiNewton algorithm
Finite difference
Application of the block backward differential formula for numerical solution of Volterra integrodifferential equations
2
2
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra IntegroDifferential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability region of orders 2, 3 and 4 are constructed which are suitable for solving stiff VIDEs.
1

99
100


Somayyeh
Fazeli
Marand Faculty of Engineering, University of Tabriz, TabrizIran
Marand Faculty of Engineering, University
I. R. Iran
fazeli@tabrizu.ac.ir
Volterra integrodifferential equations
Block methods
Backward differential formula
Numerical solution of timedependent foam drainage equation (FDE)
2
2
Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear timedependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear partial differential equations (PDEs), it can be applied very easily and it has less computational work than other existing methods like Adomian decomposition and Laplace decomposition. Additionally, effectiveness and precision of RDTM solutions are shown in tables and graphically.
1

111
122


Murat
Gubes
Karamanoglu Mehmetbey University, Department of Mathematics,Yunus Emre Campus,
70100, Karaman / Turkey
Karamanoglu Mehmetbey University, Department
Turkey
mgubes@kmu.edu.tr


Yildiray
Keskin
Selcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / Turkey
Selcuk University, Department of Mathematics,
Turkey
ykeskin@selcuk.edu.tr


Galip
Oturanc
Selcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / Turkey
Selcuk University, Department of Mathematics,
Turkey
goturanc@selcuk.edu.tr
Foam Drainage Equation
Laplace Decomposition Method
Adomian Decomposition Method
Reduced Differential Transform Method
Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
2
2
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0<t<1, 2<alpha<3, x(0)= x'(0)=0, x'(1)=beta x(xi)$, where $D_{0^{+}}^{alpha}$ denotes the standard RiemannLiouville fractional derivative,$0<xi<1$ and $0<betaxi^{alpha1}<alpha1$ Our analysis relies a fixed point theorem in partially ordered sets. An illustrative example is also presented.
1

123
133


Rahmat
Darzi
Department of Mathematics, Neka Branch,
Islamic Azad University, Neka, Iran
Department of Mathematics, Neka Branch,
Islamic
I. R. Iran
r.darzi@iauneka.ac.ir


Bahram
Agheli
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
Department of Mathematics, Qaemshahr Branch,
I. R. Iran
b.agheli@yahoo.com
Boundary value problem
fixed point theorem
Partially ordered set
Positive solution
nondecreasing solution
Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)dimension
2
2
As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of associated linear problem or Lax pair are presented in straightforward manner and finally for proposed nonlinear equation, explicit one, two and three soliton solutions are also obtained.
1

134
146


Manjit
Singh
Yadawindra College of Engineering,
Punjabi University Guru Kashi Campus,
Talwandi Sabo151302, Punjab, India
Yadawindra College of Engineering,
Punjabi
India
manjitcsir@gmail.com
Soliton solutions
Bilinear Backlund transformations
Lax pairs
Perturbation expansion