University of TabrizComputational Methods for Differential Equations2345-39825320170701Simulations of transport in one dimension1892006262ENAlper KorkmazDepartment of Mathematics,
C¸ ankırı Karatekin University, C¸ ankırı, TurkeyJournal Article20170111Advection-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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825320170701Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type2012136263ENOmid Farkhondeh RouzFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranDavood AhmadianFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20170404This 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825320170701Some new families of definite polynomials and the composition conjectures2142236266ENRazie Shafeii LashkarianDepartment of Basic science, Hashtgerd Branch,
Islamic Azad University, Alborz, IranDariush Behmardi SharifabadDepartment of Mathematics,
Alzahra university, Tehran, IranJournal Article20161115The 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825320170701Option pricing under the double stochastic volatility with double jump model2242316279ENElham DastranjDepartment of Mathematics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, IranRoghaye LatifiDepartment of Mathematics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, IranJournal Article20170112In 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825320170701The existence result of a fuzzy implicit integro-differential equation in semilinear Banach space2322456280ENMasoumeh ZeinaliFaculty of mathematical sciences, University of Tabriz, Tabriz, IranJournal Article20170223In 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.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39825320170701Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs2462556264ENArman AghiliDepartment of Applied Mathematics, Faculty of Mathematical Sciences
University of Guilan, Rasht, Iran. P. O. Box 1841Journal Article20161015Abstract. 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