eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2017-07-01
5
3
189
200
6262
Simulations of transport in one dimension
Alper Korkmaz
korkmazalper@yandex.com
1
Department of Mathematics, C¸ ankırı Karatekin University, C¸ ankırı, Turkey
Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. In the first case, pure advection conservative model problem is studied. The second problem models motion of nonconservative substance and simulates fade out of it as time proceeds. The errors between analytical and numerical results are measured by discrete maximum norm. Comparison with some earlier works indicates that the proposed algorithms generate more accurate and valid results for some discretization parameters.
http://cmde.tabrizu.ac.ir/article_6262_adc648555df00eb410f16eb851d5d001.pdf
Advection-dispersion equation
transport
pollution
Sine cardinal functions
Differential quadrature method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2017-07-01
5
3
201
213
6263
Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
Omid Farkhondeh Rouz
omid_farkhonde_7088@yahoo.com
1
Davood Ahmadian
davod_ahmadian85@yahoo.com
2
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some restrictive conditions on stepsize $delta$, drift and diffusion coefficients, but the SIE method can reproduce the exponential mean-square stability unconditionally. Moreover, for sufficiently small stepsize, we show that the decay rate as measured by the Lyapunov exponent can be reproduced arbitrarily accurately. Finally, numerical experiments are included to confirm the theorems.
http://cmde.tabrizu.ac.ir/article_6263_5ce76ae675ed3f591df2c191f12c3d50.pdf
Neutral stochastic delay differential equations
Exponential mean-square stability
Split-step (theta
lambda)-backward Euler method
Lyapunov exponent
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2017-07-01
5
3
214
223
6266
Some new families of definite polynomials and the composition conjectures
Razie Shafeii Lashkarian
razie_sh@yahoo.com
1
Dariush Behmardi Sharifabad
behmardi@alzahra.ac.ir
2
Department of Basic science, Hashtgerd Branch, Islamic Azad University, Alborz, Iran
Department of Mathematics, Alzahra university, Tehran, Iran
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjecture and the moment vanishing problem ask for that the composition condition is a necessary condition to have the center or vanishing the moments. It is not known that if there exist examples of polynomials that satisfy the double moment conditions but don't satisfy the composition condition. In this paper we consider some composition conjectures and give some families of definite polynomials for which vanishing of the moments and the composition condition are equivalent. Our methods are based on a decomposition method for continuous functions. We give an orthogonal basis for the family of continuous functions and study the conjecture in terms of this decomposition.
http://cmde.tabrizu.ac.ir/article_6266_311deb2c575c0be337945cb0844190c3.pdf
Abel equation
composition condition
composition conjecture
definite polynomial
moment
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2017-07-01
5
3
224
231
6279
Option pricing under the double stochastic volatility with double jump model
Elham Dastranj
dastranj.e@gmail.com
1
Roghaye Latifi
roghayelatifi95@yahoo.com
2
Department of Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Department of Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
In this paper, we deal with the pricing of power options when the dynamics of the risky underling asset follows the double stochastic volatility with double jump model. We prove efficiency of our considered model by fast Fourier transform method, Monte Carlo simulation and numerical results using power call options i.e. Monte Carlo simulation and numerical results show that the fast Fourier transform is correct.
http://cmde.tabrizu.ac.ir/article_6279_cd940f979091503956ffb28024cef95e.pdf
Power option
Monte Carlo
Fast Fourier Transform
Double Stochastic Volatility
Double Jump
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2017-07-01
5
3
232
245
6280
The existence result of a fuzzy implicit integro-differential equation in semilinear Banach space
Masoumeh Zeinali
zeinali@tabrizu.ac.ir
1
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
In this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integro-differential equation arising in the field of fluid mechanics is investigated. First, an equivalency lemma is presented by which the problem understudy is converted to the two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions required to guarantee the existence of a solution for the equivalent integral equation are investigated using the Schauder fixed point theorem in semilinear Banach space.
http://cmde.tabrizu.ac.ir/article_6280_4f3906a00a160ec0367009ea7c9e91eb.pdf
Implicit fuzzy integro-differential equation
Semilinear Banach space
Schauder fixed point theorem
Generalized differentiability
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2017-07-01
5
3
246
255
6264
Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
Arman Aghili
arman.aghili@gmail.com
1
Department of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, Iran. P. O. Box 1841
Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the combined use of integral transforms and exponential operator method is very efficient tool in finding exact solutions for ordinary and partial differential equations with fractional order. Finally, illustrative examples are also provided.
http://cmde.tabrizu.ac.ir/article_6264_d2e4727a6beb591cee79f9e6a10865c7.pdf
fractional partial differential equations
Exponential operational method
Riemann - Liouville fractional derivative
Laplace transform
Caputo fractional derivative