University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
The Legendre Wavelet Method for Solving Singular Integro-differential Equations
62
68
EN
Naser
Aghazadeh
Azarbaijan Shahid Madani University
aghazadeh@azaruniv.ac.ir
Yasser
Gholizade Atani
Azarbaijan
Shahid Madani University
yasermat.2010@gmail.com
Parisa
Noras
Azarbaijan
Shahid Madani University
a@bc.com
In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.
Legendre wavelet,Singular integro-differential equation,Cauchy type
http://cmde.tabrizu.ac.ir/article_1684.html
http://cmde.tabrizu.ac.ir/article_1684_8e7ffce39655216dddcfcee75de575d1.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
Exact solutions of the 2D Ginzburg-Landau equation by the first integral method
69
76
EN
Ahmet
Bekir
Eskisehir Osmangazi University, Art-Science Faculty,
Department of Mathematics-Computer
abekir@ogu.edu.tr
Abdelfattah
El Achab
University of Choua¨ıb Doukkali
abdelfattahelachab@gmail.com
The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.
exact solutions,First integral method,2D Ginzburg-Landau equation
http://cmde.tabrizu.ac.ir/article_1888.html
http://cmde.tabrizu.ac.ir/article_1888_ae6174f1516ae4870160a055be8df5de.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
New study to construct new solitary wave solutions for generalized sinh- Gordon equation
77
82
EN
Ahmad
Neirameh
Gonbad Kavous University
a.neirameh@guilan.ac.ir
Saeed
Shokooh
Gonbad Kavous University
shokooh.sd@gmail.com
In this work, we successfully construct the new exact traveling wave solutions of the generalized Sinh–Gordon equation by new application of the homogeneous balance method. The idea introduced in this paper can be applied to other nonlinear evolution equations.
Solitary wave solution,Homogeneous balance method,generalized sine-Gordon equation
http://cmde.tabrizu.ac.ir/article_1889.html
http://cmde.tabrizu.ac.ir/article_1889_51dcd9268fe386fe8f6c2ba01565a822.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
The extended homogeneous balance method and exact solutions of the Maccari system
83
90
EN
Mohammad
Mirzazadeh
Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
mirzazadehs2@guilan.ac.ir
The extended homogeneous balance method is used to construct exact traveling wave solutions of the Maccari system, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Maccari system equation are successfully obtained.
Extended homogeneous balance method,Maccari system,Riccati equation,Soliton-like solution,Periodic-like solution
http://cmde.tabrizu.ac.ir/article_1890.html
http://cmde.tabrizu.ac.ir/article_1890_9b1a45799a08eefd34fd63ea5532dcd6.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
A new total variation diminishing implicit nonstandard finite difference scheme for conservation laws
91
98
EN
Mohammad
Mehdizadeh Khalsaraei
University of Maragheh
muhammad.mehdizadeh@gmail.com
F.
Khodadosti
0000-0003-4315-3907
University of Maragheh
fayyaz64dr@gmail.com
In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities. Numerical results for Burger's equation is presented. Comparison of numerical results with a classical difference scheme is given.
Nonstandard finite difference scheme,Total variation diminishing,Conservation law,Nonlocal approximation
http://cmde.tabrizu.ac.ir/article_2389.html
http://cmde.tabrizu.ac.ir/article_2389_287b8f7baa7e4c82cd846d99277a21c6.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
Analytical solutions for the fractional Klein-Gordon equation
99
114
EN
Hosseni
Kheiri
University of Tabriz
kheirihossein@yahoo.com
Samane
Shahi
University of Tabriz
samanesh7@gmail.com
Aida
Mojaver
University of Tabriz
aida_mojaver1987@yahoo.com
In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.
Fractional Klein-Gordon equation,Mittag-Leffler,Method of separating variables,Caputo derivative
http://cmde.tabrizu.ac.ir/article_2497.html
http://cmde.tabrizu.ac.ir/article_2497_7dd788eed92aa45961fd50bea239e6ee.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
2
2014
04
01
Solitary Wave solutions to the (3+1)-dimensional Jimbo Miwa equation
115
122
EN
Mostafa
Eslami
University of Mazandaran, Iran
mostafa.eslami@umz.ac.ir
The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.
Homogeneous balance method,(3+1) Jimbo–Miwa equation,Solitary wave solutions
http://cmde.tabrizu.ac.ir/article_2390.html
http://cmde.tabrizu.ac.ir/article_2390_058bb0778cbfad9728f30dee61ea807a.pdf