University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
Solving nonlinear space-time fractional differential equations via ansatz method
1
11
EN
Ozkan
Guner
Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri, Turkey
ozkanguner@karatekin.edu.tr
Ahmet
Bekir
Eskisehir Osmangazi University, Art-Science Faculty,
Department of Mathematics-Computer, Eskisehir, Turkey
abekir@ogu.edu.tr
In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuznetsov Benjamin Bona Mahony (ZK-BBM) equation, the space-time fractional Klein-Gordon equation and the space-time fractional modified Regularized Long Wave (RLW) equation. This method can be suitable and more powerful for solving other kinds of nonlinear FDEs arising in mathematical physics.
Ansatz method,Exact solution,Space-time fractional differential equations
http://cmde.tabrizu.ac.ir/article_6814.html
http://cmde.tabrizu.ac.ir/article_6814_902aea215aaea02094195f2d1fb3b886.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
Exact solutions of a linear fractional partial differential equation via characteristics method
12
18
EN
Elham
Lashkarian
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
lashkarianelham@yahoo.com
Seyed Reza
Hejazi
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
ra.hejazi@gmail.com
In recent years, many methods have been studied for solving differential equations of fractional order, such as Lie group method, invariant subspace method and numerical methods, cite{6,5,7,8}. Among this, the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order. In this paper we apply this method for solving a family of linear (2+1)-dimensional FDE of multi order $alpha,beta$ and $gamma$.
Fractional derivatives,Mittag-Leffler function,Characteristics method
http://cmde.tabrizu.ac.ir/article_6807.html
http://cmde.tabrizu.ac.ir/article_6807_1f8b6308a4d5f4bb27bd1b83f2252a51.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
Inverse nodal problem for p-Laplacian with two potential functions
19
29
EN
Abdol Hadi
Dabbaghian
Department of Mathematics, Neka Branch,
Islamic Azad University, Neka, Iran
a.dabbaghian@umz.ac.ir
In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of inverse nodal problem when the two potential functions are unknown.
Prufer substitution,Inverse nodal problem,P-Laplacian operator
http://cmde.tabrizu.ac.ir/article_6806.html
http://cmde.tabrizu.ac.ir/article_6806_50b2729eb0e3672370769ec0cb6ff0c4.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
On asymptotic stability of Weber fractional differential systems
30
39
EN
Mohammad Hossein
Derakhshan
Department of Applied Mathematics, Faculty of Mathematical Sciences
Shahrekord University, P.O.Box 115, Shahrekord, Iran
m.h.derakhshan.20@gmail.com
Alireza
Ansari
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P.O.Box 115, Shahrekord
alireza_1038@yahoo.com
Mohammadreza
Ahmadi Darani
Department of Applied Mathematics, Faculty of Mathematical Sciences
Shahrekord University, P.O.Box 115, Shahrekord, Iran
farshidahmadi633@gmail.com
In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.
Asymptotically stable,Weber fractional derivative,Riemann-Liouville fractional derivative
http://cmde.tabrizu.ac.ir/article_6808.html
http://cmde.tabrizu.ac.ir/article_6808_ed8910a8567d8b6fc229377a444ddb36.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
A novel technique for a class of singular boundary value problems
40
52
EN
Mohammad Hadi
Noori Skandari
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
math.noori@yahoo.com
Mehrdad
Ghaznavi
Faculty of Mathematical Sciences, Shahrood University of Sciences, Shahrood, Iran
ghaznavi@shahroodut.ac.ir
In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time optimization problem to a discrete time optimization problem. By solving the discrete time optimization problem, we find discrete approximations for the solutions of the main singular boundary value problem. Also, by Lagrange interpolation we obtain a continuous approximation for the solution. The efficiency and the reliability of the proposed approach are tested by solving three practical singular boundary value problems.
Singular boundary value problem,Chebyshev polynomial,Continuous time optimization problem,Discrete optimization problem
http://cmde.tabrizu.ac.ir/article_6813.html
http://cmde.tabrizu.ac.ir/article_6813_989cc111ad88bd05f7c74654f1bbdbe6.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
Numerical treatment for nonlinear steady flow of a third grade fluid in a porous half space by neural networks optimized
53
62
EN
Mohsen
Alipour
Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave.,
Babol, Iran, Post Code: 47148-71167
m.alipour@nit.ac.ir
Kobra
Karimi
Deprtment of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
kobra.karimi@yahoo.com
In this paper, steady flow of a third-grade fluid in a porous half space has been considered. This problem is a nonlinear two-point boundary value problem (BVP) on semi-infinite interval. The solution for this problem is given by a numerical method based on the feed-forward artificial neural network model using radial basis activation functions trained with an interior point method. Moreover, to confirm the performance of the proposed technique, our results are compared with other available results. Numerical results demonstrate the validity and applicability of the technique.
Feed forward neural network,Radial basis functions,Semi infinite,Steady flow,Third-grade fluid
http://cmde.tabrizu.ac.ir/article_6815.html
http://cmde.tabrizu.ac.ir/article_6815_e120001746c4d99862eb7e2964d70abc.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
European and American put valuation via a high-order semi-discretization scheme
63
79
EN
Farshad
Kiyoumarsi
Faculty of Basic Science, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
kumarci_farshad@yahoo.com
Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accuracy is constructed for the problem of European and American put options. Several numerical experiments are also worked out.
Option pricing,Numerical scheme,Black-Scholes PDE,Semi-discretization,Put option
http://cmde.tabrizu.ac.ir/article_6809.html
http://cmde.tabrizu.ac.ir/article_6809_bbf4c96b3c828a3536425fe225457590.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations
80
97
EN
Farshid
Mirzaee
0000-0002-1429-2548
Faculty of Mathematical Sciences and Statistics, Malayer University,
P. O. Box 65719-95863, Malayer, Iran
f.mirzaee@malayeru.ac.ir
Nasrin
Samadyar
Faculty of Mathematical Sciences and Statistics, Malayer University,
Malayer, Iran
nasrin.samadyar@stu.malayeru.ac.ir
In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to the nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. Convergence analysis with error estimate are given with full discussion. Also, we provide an upper error bound under weak assumptions. Finally, accuracy of this scheme is checked with two numerical examples. The obtained results reveal efficiency and capability of the proposed method.
Stochastic integrals,Operational matrix of integration,Wavelet,Legendre polynomials,Error analysis
http://cmde.tabrizu.ac.ir/article_6816.html
http://cmde.tabrizu.ac.ir/article_6816_c11298fd2bfce8fb0588a4e94fae98d8.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
6
1
2018
01
01
A numerical investigation of a reaction-diffusion equation arises from an ecological phenomenon
98
110
EN
Parastoo
Reihani
Department of Mathematics, Payame Noor University, Tehran, Iran
p_reihani@pnu.ac.ir
This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include interactions between species may restricts to pairwise interactions. Three mathematical models of invasions of species in more complex settings that include interactions between species are introduced. For one of these models in general form a computational approach based on finite difference and RBF collocation method is established. To numerical solution first we discretize the proposed equations by using the forward difference rule for time derivatives and the well known Crank-Nicolson scheme for other terms between successive time levels. To verify the ability and robustness of the numerical approach, two test problems are investigated.
Ecological phenomena,Reaction-diffusion,Invasion,RBF collocation,Finite differences method
http://cmde.tabrizu.ac.ir/article_6823.html
http://cmde.tabrizu.ac.ir/article_6823_ea8363cff773d29fc020b0d107779c5a.pdf