eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-10-01
2
4
205
215
3138
Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems
Rahmat Ali Khan
rahmat_alipk@yahoo.com
1
Aziz Khan
azizkhan927@yahoo.com
2
Department of Mathematics, University of Malaknd at Chakdara Dir Lower, Khybar Pakhtunkhwa, Pakistan
University of Peshawar, Pakistan
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.
http://cmde.tabrizu.ac.ir/article_3138_d0d51e21fca62f083313ef3d8e8382a6.pdf
Fractional differential equations
Three point boundary conditions
Fixed point theorems
p-Laplacian operator
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-10-01
2
4
216
226
3316
The B"{a}cklund transformation method of Riccati equation to coupled Higgs field and Hamiltonian amplitude equations
Ahmad Hasan Arnous
ahmed.h.arnous@gmail.com
1
Mohammad Mirzazadeh
mirzazadehs2@guilan.ac.ir
2
Mostafa Eslami
mostafa.eslami@umz.ac.ir
3
Department of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk, Cairo, Egypt
Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
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.
http://cmde.tabrizu.ac.ir/article_3316_ee955e00f9d31c2df0030b5e9eb6adc2.pdf
Complex nonlinear wave equations
exact solutions
B"{a}cklund transformation method of Riccati equation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-10-01
2
4
227
242
3169
Topological soliton solutions of the some nonlinear partial differential equations
Ozkan Guner
ozkanguner@karatekin.edu.tr
1
Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri-TURKEY
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.
http://cmde.tabrizu.ac.ir/article_3169_3e9ca9ba1422f83c2e9e20459cfdf8e4.pdf
Exact solution
topological soliton solution
the (3+1)-dimensional shallow water wave equation
the symmetric regularized long wave (SRLW) equation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-10-01
2
4
243
255
3772
Generalized B-spline functions method for solving optimal control problems
Yousef Edrisi Tabriz
yedrisy@gmail.com
1
Aghileh Heydari
a_heidari@pnu.ac.ir
2
Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran
Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran
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.
http://cmde.tabrizu.ac.ir/article_3772_469ce62234092e58427d577e03b4b0d4.pdf
Optimal control problem
B-spline functions
Derivative matrix
Collocation method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-10-01
2
4
256
267
3583
Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
Mohammad Mehdizadeh Khalsaraei
muhammad.mehdizadeh@gmail.com
1
Reza Shokri Jahandizi
reza.shokri.j@gmail.com
2
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
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.
http://cmde.tabrizu.ac.ir/article_3583_bfed57f3653505f17e60608b463669be.pdf
Nonstandard finite differences
positivity
Advection-diffusion reaction equation
M-matrix
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-10-01
2
4
268
282
3834
Fractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations
Mohammadreza Ahmadi Darani
ahmadi.darani@sci.sku.ac.ir
1
Shirin Bagheri
shirinbagheri55@yahoo.com
2
Faculty of mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran.
Faculty of Basic Sciences, Islamic Azad University, Science and Research Branch, P. O. Box 14515/775, Tehran, Iran.
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.
http://cmde.tabrizu.ac.ir/article_3834_bb3f883a1e0a93f9f79e70f8f6790c93.pdf
Integro-differential equations
fractional type of flatlet oblique multiwavelets
biorthogonal flatlet multiwavelet system