University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
1
2016
01
01
Threshold harvesting policy and delayed ratio-dependent functional response predator-prey model
1
18
EN
Razie
Shafeii Lashkarian
Department of Basic science, Hashtgerd Branch,
Islamic Azad University, Alborz, Iran
razie_sh@yahoo.com
Dariush
Behmardi Sharifabad
Department of Mathematics,
Alzahra university, Tehran, Iran
behmardi@alzahra.ac.ir
This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties are examined too. Then we analyze the effect of time delay on the stabilization of the equilibria, i.e., we study whether time delay could change the stability of a co-existence point from an unstable mood to a stable one. The system undergoes a Hopf bifurcation when it passes a critical time delay. Finally, some numerical simulations are performed to support our analytic results.
Predator-prey model,ratio-dependent functional response,threshold harvesting,time delay,Hopf bifurcation
http://cmde.tabrizu.ac.ir/article_5428.html
http://cmde.tabrizu.ac.ir/article_5428_fa1f77b2c0cba4797f160a0a7a448e19.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
1
2016
01
01
Existence of positive solution to a class of boundary value problems of fractional differential equations
19
29
EN
Amjad
Ali
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
amjadalimna@yahoo.com
Kamal
Shah
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
kamalshah408@gmail.com
Rahmat Ali
Khan
Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
rahmat_alipk@yahoo.com
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Thank to classical fixed point theorems of nonlinear alternative of Leray-Schauder and Banach Contraction principle, sufficient conditions are developed under which the proposed problem has at least one solution. An example has been provided to illustrate the main results.
Boundary value problem,Existence and uniqueness results,Fractional differential differential equations,Classical fixed point theorem
http://cmde.tabrizu.ac.ir/article_5429.html
http://cmde.tabrizu.ac.ir/article_5429_e4b51aaaf607a9dc32a0613553911566.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
1
2016
01
01
An approach based on statistical spline model for Volterra-Fredholm integral equations
30
42
EN
Amir Hossein
Salehi Shayegan
Faculty of Mathematics, K. N. Toosi University of Technology,
P. O. Box 16315 − 1618, Tehran, Iran
ah.salehi@mail.kntu.ac.ir
Ali
Zakeri
Faculty of Mathematics, K. N. Toosi University of Technology,
P. O. Box 16315 − 1618, Tehran, Iran
azakeri@kntu.ac.ir
M. R.
Peyghami
Faculty of Mathematics, K. N. Toosi University of Technology,
P. O. Box 16315 − 1618, Tehran, Iran
peyghami@kntu.ac.ir
In this paper, an approach based on statistical spline model (SSM) and collocation method is proposed to solve Volterra-Fredholm integral equations. The set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials. Under some standard assumptions, we establish the convergence property of this approach. Numerical results on some problems are given to describe the introduced method. A comparison between the numerical results and those obtained from Lagrange and Taylor collocation methods demonstrates that the proposed method generates an approximate solution with minimal error.
Statistical spline model,Volterra-Fredholm integral equations,Convergence analysis
http://cmde.tabrizu.ac.ir/article_5441.html
http://cmde.tabrizu.ac.ir/article_5441_a9657fe62ac81db659aa73c9a11cdc0f.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
1
2016
01
01
The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation
43
53
EN
Zainab
Ayati
Department of Engineering sciences,
Faculty of Technology and Engineering East of Guilan,
University of Guilan P.C.44891-Rudsar-Vajargah,Iran
ayati.zainab@gmail.com
Sima
Ahmady
Department of Mathematics, Payame Noor University,
P.O.Box 19395-3697, Tehran, Iran
sima.ahmadikia@gmail.com
In recent years, numerous approaches have been applied for ﬁnding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the results of homotopy Perturbation method.
Optimal Homotopy Asymptotic method,Homotopy Perturbation method,Fisher equation
http://cmde.tabrizu.ac.ir/article_5442.html
http://cmde.tabrizu.ac.ir/article_5442_1274a06c80df611c4fca84aea6dcd196.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
1
2016
01
01
On the split-step method for the solution of nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative
54
69
EN
Akbar
Mohebbi
Department of Applied Mathematics,
Faculty of Mathematical Science,
University of Kashan, Kashan, Iran
a_mohebbi@kashanu.ac.ir
The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-Nicolson and a split-step methods to obtain a numerical method for this equation. In the proposed method there is no need to solve the nonlinear system of algebraic equations and the method is convergent and unconditionally stable. The proposed method preserves the discrete mass which will be investigated numerically. Numerical results demonstrate the reliability, accuracy and efficiency of the proposed method.
Finite difference method,Riesz space fractional derivatives,Unconditional stability,Schr"{o}dinger equation
http://cmde.tabrizu.ac.ir/article_5443.html
http://cmde.tabrizu.ac.ir/article_5443_cedd8d12d1c83ea1861e67cef8734362.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
1
2016
01
01
Analytical solution of MHD flow and heat transfer over a permeable nonlinearly stretching sheet in a porous medium filled by a nanofluid
70
98
EN
Amir
Parsa
Department of Mechanical Engineering,
Bu-Ali Sina University,
Hamedan, Iran
amirbparsa@yahoo.com
Habib-Olah
Sayehvand
Department of Mechanical Engineering,
Bu-Ali Sina University,
Hamedan, Iran
hsayehvand@yahoo.com
In this paper, the differential transform method and Padé approximation (DTM-Padé) is applied to obtain the approximate analytical solutions of the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved by DTM-Padé and validity of our solutions is verified by the numerical results (fourth-order Runge-Kutta scheme with the shooting method). The stretching velocity of sheet is assumed to have a power-law variation with the horizontal distance along the plate. It was shown that the differential transform method (DTM) solutions are only valid for small values of independent variable but the obtained results by the DTM-Padé are valid for the whole solution domain with high accuracy. Finally, the analytical solutions of the problem for different values of the fixed parameters are shown and discussed. Furthermore, it is found that permeability parameter of medium has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.
DTM-Padé,MHD,Nanofluid,Porous medium,Prescribed temperature
http://cmde.tabrizu.ac.ir/article_5444.html
http://cmde.tabrizu.ac.ir/article_5444_3b8dd28d47f63c309745589a4a13de10.pdf