University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
4
2014
10
01
Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems
205
215
EN
Rahmat
Ali Khan
Department of Mathematics, University of Malaknd at Chakdara Dir Lower, Khybar Pakhtunkhwa, Pakistan
rahmat_alipk@yahoo.com
Aziz
Khan
University of Peshawar, Pakistan
azizkhan927@yahoo.com
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
Fractional differential equations,Three point boundary conditions,Fixed point theorems,p-Laplacian operator
http://cmde.tabrizu.ac.ir/article_3138.html
http://cmde.tabrizu.ac.ir/article_3138_d0d51e21fca62f083313ef3d8e8382a6.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
4
2014
10
01
The B"{a}cklund transformation method of Riccati equation to coupled Higgs field and Hamiltonian amplitude equations
216
226
EN
Ahmad Hasan
Arnous
Department of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk, Cairo, Egypt
ahmed.h.arnous@gmail.com
Mohammad
Mirzazadeh
Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
mirzazadehs2@guilan.ac.ir
Mostafa
Eslami
Department of Mathematics,
Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
mostafa.eslami@umz.ac.ir
In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathematical physics and engineering sciences. Obtained solutions may also be important of significance for the explanation of some practical physical problems.
Complex nonlinear wave equations,exact solutions,B"{a}cklund transformation method of Riccati equation
http://cmde.tabrizu.ac.ir/article_3316.html
http://cmde.tabrizu.ac.ir/article_3316_ee955e00f9d31c2df0030b5e9eb6adc2.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
4
2014
10
01
Topological soliton solutions of the some nonlinear partial differential equations
227
242
EN
Ozkan
Guner
Cankiri Karatekin University, Faculty of Economics and Administrative Sciences,
Department of International Trade, Cankiri-TURKEY
ozkanguner@karatekin.edu.tr
In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note that, this method is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.
Exact solution,topological soliton solution,the (3+1)-dimensional shallow water wave equation,the symmetric regularized long wave (SRLW) equation
http://cmde.tabrizu.ac.ir/article_3169.html
http://cmde.tabrizu.ac.ir/article_3169_3e9ca9ba1422f83c2e9e20459cfdf8e4.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
4
2014
10
01
Generalized B-spline functions method for solving optimal control problems
243
255
EN
Yousef
Edrisi Tabriz
Department of Mathematics,
Payame Noor University,
PO BOX 19395-3697, Tehran, Iran
yedrisy@gmail.com
Aghileh
Heydari
Department of Mathematics,
Payame Noor University,
PO BOX 19395-3697, Tehran, Iran
a_heidari@pnu.ac.ir
In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our heoretical findings.
Optimal control problem,B-spline functions,Derivative matrix,Collocation method
http://cmde.tabrizu.ac.ir/article_3772.html
http://cmde.tabrizu.ac.ir/article_3772_469ce62234092e58427d577e03b4b0d4.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
4
2014
10
01
Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
256
267
EN
Mohammad
Mehdizadeh Khalsaraei
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
muhammad.mehdizadeh@gmail.com
Reza
Shokri Jahandizi
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
reza.shokri.j@gmail.com
Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawbacks such as spurious oscillations and negative solutions because of truncation errors and may then become unstable. we propose a new scheme that guarantees a smooth numerical solution, free of spurious oscillations and satisfies the positivity requirement, as is demanded for the advection-diffusion reaction equations. The method is applicable to both advection and diffusion dominated problems. We give some examples from different applications.
Nonstandard finite differences,positivity,Advection-diffusion reaction equation,M-matrix
http://cmde.tabrizu.ac.ir/article_3583.html
http://cmde.tabrizu.ac.ir/article_3583_bfed57f3653505f17e60608b463669be.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
4
2014
10
01
Fractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations
268
282
EN
Mohammadreza
Ahmadi Darani
Faculty of mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran.
ahmadi.darani@sci.sku.ac.ir
Shirin
Bagheri
Faculty of Basic Sciences, Islamic Azad University, Science and Research Branch,
P. O. Box 14515/775, Tehran, Iran.
shirinbagheri55@yahoo.com
The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test problems are discussed at the end of paper to show the efficiency of the proposed method.
Integro-differential equations,fractional type of flatlet oblique multiwavelets,biorthogonal flatlet multiwavelet system
http://cmde.tabrizu.ac.ir/article_3834.html
http://cmde.tabrizu.ac.ir/article_3834_bb3f883a1e0a93f9f79e70f8f6790c93.pdf