2017
5
3
3
67
Simulations of transport in one dimension
2
2
Advectiondispersion 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.
1

189
200


Alper
Korkmaz
Department of Mathematics,
C¸ ankırı Karatekin University, C¸ ankırı, Turkey
Department of Mathematics,
C¸ ankırı
Turkey
korkmazalper@yandex.com
Advectiondispersion equation
transport
pollution
Sine cardinal functions
Differential quadrature method
Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
2
2
This paper examines stability analysis of two classes of improved backward Euler methods, namely splitstep $(theta, lambda)$backward Euler (SSBE) and semiimplicit $(theta,lambda)$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 meansquare stability with some restrictive conditions on stepsize $delta$, drift and diffusion coefficients, but the SIE method can reproduce the exponential meansquare 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.
1

201
213


Omid
Farkhondeh Rouz
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University
I. R. Iran
omid_farkhonde_7088@yahoo.com


Davood
Ahmadian
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University
I. R. Iran
davod_ahmadian85@yahoo.com
Neutral stochastic delay differential equations
Exponential meansquare stability
Splitstep (theta
lambda)backward Euler method
Lyapunov exponent
Some new families of definite polynomials and the composition conjectures
2
2
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.
1

214
223


Razie
Shafeii Lashkarian
Department of Basic science, Hashtgerd Branch,
Islamic Azad University, Alborz, Iran
Department of Basic science, Hashtgerd Branch,
Isl
I. R. Iran
razie_sh@yahoo.com


Dariush
Behmardi Sharifabad
Department of Mathematics,
Alzahra university, Tehran, Iran
Department of Mathematics,
Alzahra university,
I. R. Iran
behmardi@alzahra.ac.ir
Abel equation
composition condition
composition conjecture
definite polynomial
moment
Option pricing under the double stochastic volatility with double jump model
2
2
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.
1

224
231


Elham
Dastranj
Department of Mathematics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, Iran
Department of Mathematics, Faculty of Mathematical
I. R. Iran
dastranj.e@gmail.com


Roghaye
Latifi
Department of Mathematics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, Iran
Department of Mathematics, Faculty of Mathematical
I. R. Iran
roghayelatifi95@yahoo.com
Power option
Monte Carlo
Fast Fourier Transform
Double Stochastic Volatility
Double Jump
The existence result of a fuzzy implicit integrodifferential equation in semilinear Banach space
2
2
In this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integrodifferential 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.
1

232
245


Masoumeh
Zeinali
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
Faculty of mathematical sciences, University
I. R. Iran
zeinali@tabrizu.ac.ir
Implicit fuzzy integrodifferential equation
Semilinear Banach space
Schauder fixed point theorem
Generalized differentiability
Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
2
2
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 nonconstant 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.
1

246
255


Arman
Aghili
Department of Applied Mathematics, Faculty of Mathematical Sciences
University of Guilan, Rasht, Iran. P. O. Box 1841
Department of Applied Mathematics, Faculty
I. R. Iran
arman.aghili@gmail.com
fractional partial differential equations
Exponential operational method
Riemann  Liouville fractional derivative
Laplace transform
Caputo fractional derivative