University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
2
2015
04
01
Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
70
86
EN
Mina
Mortazavi
Department of Applied Mathematics,
School of Mathematical Sciences,
Ferdowsi University of Mashhad,
Mashhad, Iran
m_mortazavi95@yahoo.com
Mohammad
Mirzazadeh
Department of Mathematics,
Faculty of Mathematical Sciences,
University of Guilan, Rasht, Iran
mirzazadehs2@guilan.ac.ir
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.
Exact traveling wave Solutions,Modified Complex Ginzburg-Landau equation,$(G'/G)$-expanson method,Homogeneous balance method,Eextended F-expansion method
http://cmde.tabrizu.ac.ir/article_4017.html
http://cmde.tabrizu.ac.ir/article_4017_0464648f9f5a70082b84fd3112ca2dcf.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
2
2015
04
01
Optimization with the time-dependent Navier-Stokes equations as constraints
87
98
EN
Mitra
Vizheh
Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran
mitravizheh@gmail.com
Syaed Hodjatollah
Momeni-Masuleh
Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran
momeni@shahed.ac.ir
Alaeddin
Malek
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: 14115-134, Iran
mala@modares.ac.ir
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.
Optimal Control Problems,Navier-Stokes equations,PDE-constrained optimization,quasi-Newton algorithm,finite difference
http://cmde.tabrizu.ac.ir/article_4484.html
http://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
2
2015
04
01
Application of the block backward differential formula for numerical solution of Volterra integro-differential equations
99
100
EN
Somayyeh
Fazeli
Marand Faculty of Engineering, University of Tabriz, Tabriz-Iran
fazeli@tabrizu.ac.ir
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.
Volterra integro-differential equations,Block methods,Backward differential formula
http://cmde.tabrizu.ac.ir/article_4541.html
http://cmde.tabrizu.ac.ir/article_4541_07598b31f5bf268f9053f664f3870864.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
2
2015
04
01
Numerical solution of time-dependent foam drainage equation (FDE)
111
122
EN
Murat
Gubes
Karamanoglu Mehmetbey University, Department of Mathematics,Yunus Emre Campus,
70100, Karaman / Turkey
mgubes@kmu.edu.tr
Yildiray
Keskin
Selcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / Turkey
ykeskin@selcuk.edu.tr
Galip
Oturanc
Selcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / Turkey
goturanc@selcuk.edu.tr
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.
Foam Drainage Equation,Laplace Decomposition Method,Adomian Decomposition Method,Reduced Differential Transform Method
http://cmde.tabrizu.ac.ir/article_4648.html
http://cmde.tabrizu.ac.ir/article_4648_efda79e599c82bb21304dce4c2502549.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
2
2015
04
01
Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
123
133
EN
Rahmat
Darzi
Department of Mathematics, Neka Branch,
Islamic Azad University, Neka, Iran
r.darzi@iauneka.ac.ir
Bahram
Agheli
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
b.agheli@yahoo.com
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
Boundary value problem,fixed point theorem,Partially ordered set,Positive solution,nondecreasing solution
http://cmde.tabrizu.ac.ir/article_4649.html
http://cmde.tabrizu.ac.ir/article_4649_30ab2f42a41eb1f68dba3f0aab9d34fc.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
2
2015
04
01
Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimension
134
146
EN
Manjit
Singh
Yadawindra College of Engineering,
Punjabi University Guru Kashi Campus,
Talwandi Sabo-151302, Punjab, India
manjitcsir@gmail.com
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.
Soliton solutions,Bilinear Backlund transformations,Lax pairs,Perturbation expansion
http://cmde.tabrizu.ac.ir/article_4769.html
http://cmde.tabrizu.ac.ir/article_4769_c037a3bd2246ff1cd130bac4856a2745.pdf