eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-04-01
3
2
70
86
4017
Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
Mina Mortazavi
m_mortazavi95@yahoo.com
1
Mohammad Mirzazadeh
mirzazadehs2@guilan.ac.ir
2
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, 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.
http://cmde.tabrizu.ac.ir/article_4017_0464648f9f5a70082b84fd3112ca2dcf.pdf
Exact traveling wave Solutions
Modified Complex Ginzburg-Landau equation
$(G'/G)$-expanson method
Homogeneous balance method
Eextended F-expansion method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-04-01
3
2
87
98
4484
Optimization with the time-dependent Navier-Stokes equations as constraints
Mitra Vizheh
mitravizheh@gmail.com
1
Syaed Hodjatollah Momeni-Masuleh
momeni@shahed.ac.ir
2
Alaeddin Malek
mala@modares.ac.ir
3
Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran
Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: 14115-134, Iran
In this paper, optimal distributed control of the time-dependent Navier-Stokes 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 quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.
http://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdf
Optimal Control Problems
Navier-Stokes equations
PDE-constrained optimization
quasi-Newton algorithm
Finite difference
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-04-01
3
2
99
100
4541
Application of the block backward differential formula for numerical solution of Volterra integro-differential equations
Somayyeh Fazeli
fazeli@tabrizu.ac.ir
1
Marand Faculty of Engineering, University of Tabriz, Tabriz-Iran
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential 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.
http://cmde.tabrizu.ac.ir/article_4541_07598b31f5bf268f9053f664f3870864.pdf
Volterra integro-differential equations
Block methods
Backward differential formula
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-04-01
3
2
111
122
4648
Numerical solution of time-dependent foam drainage equation (FDE)
Murat Gubes
mgubes@kmu.edu.tr
1
Yildiray Keskin
ykeskin@selcuk.edu.tr
2
Galip Oturanc
goturanc@selcuk.edu.tr
3
Karamanoglu Mehmetbey University, Department of Mathematics,Yunus Emre Campus, 70100, Karaman / Turkey
Selcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / Turkey
Selcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / Turkey
Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent 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.
http://cmde.tabrizu.ac.ir/article_4648_efda79e599c82bb21304dce4c2502549.pdf
Foam Drainage Equation
Laplace Decomposition Method
Adomian Decomposition Method
Reduced Differential Transform Method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-04-01
3
2
123
133
4649
Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
Rahmat Darzi
r.darzi@iauneka.ac.ir
1
Bahram Agheli
b.agheli@yahoo.com
2
Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
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
http://cmde.tabrizu.ac.ir/article_4649_30ab2f42a41eb1f68dba3f0aab9d34fc.pdf
Boundary value problem
fixed point theorem
Partially ordered set
Positive solution
nondecreasing solution
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-04-01
3
2
134
146
4769
Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimension
Manjit Singh
manjitcsir@gmail.com
1
Yadawindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo-151302, Punjab, India
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.
http://cmde.tabrizu.ac.ir/article_4769_c037a3bd2246ff1cd130bac4856a2745.pdf
Soliton solutions
Bilinear Backlund transformations
Lax pairs
Perturbation expansion