Simulations of transport in one dimension
Alper
Korkmaz
Department of Mathematics,
C¸ ankırı Karatekin University, C¸ ankırı, Turkey
author
text
article
2017
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
5
v.
3
no.
2017
189
200
http://cmde.tabrizu.ac.ir/article_6262_adc648555df00eb410f16eb851d5d001.pdf
Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
Omid
Farkhondeh Rouz
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
author
Davood
Ahmadian
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
author
text
article
2017
eng
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 $\theta, \lambda\in(0,1]$ 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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
5
v.
3
no.
2017
201
213
http://cmde.tabrizu.ac.ir/article_6263_5ce76ae675ed3f591df2c191f12c3d50.pdf
Some new families of definite polynomials and the composition conjectures
Razie
Shafeii Lashkarian
Department of Basic science, Hashtgerd Branch,
Islamic Azad University, Alborz, Iran
author
Dariush
Behmardi Sharifabad
Department of Mathematics,
Alzahra university, Tehran, Iran
author
text
article
2017
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
5
v.
3
no.
2017
214
223
http://cmde.tabrizu.ac.ir/article_6266_311deb2c575c0be337945cb0844190c3.pdf
Option pricing under the double stochastic volatility with double jump model
Elham
Dastranj
Department of Mathematics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, Iran
author
Roghaye
Latifi
Department of Mathematics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, Iran
author
text
article
2017
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
5
v.
3
no.
2017
224
231
http://cmde.tabrizu.ac.ir/article_6279_cd940f979091503956ffb28024cef95e.pdf
The existence result of a fuzzy implicit integro-differential equation in semilinear Banach space
Masoumeh
Zeinali
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
author
text
article
2017
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
5
v.
3
no.
2017
232
245
http://cmde.tabrizu.ac.ir/article_6280_4f3906a00a160ec0367009ea7c9e91eb.pdf
Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
Arman
Aghili
Department of Applied Mathematics, Faculty of Mathematical Sciences
University of Guilan, Rasht, Iran. P. O. Box 1841
author
text
article
2017
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
5
v.
3
no.
2017
246
255
http://cmde.tabrizu.ac.ir/article_6264_d2e4727a6beb591cee79f9e6a10865c7.pdf