[PDF] Top 20 15. On a $q$-analogue of the one-dimensional heat equation

... D q 2 derivative [3] and the Rubin’s ∂ q -derivative [8, 9] in time and in space, respectively, and we attempt to develop the q-analogue of the theory introduced by ...as q tends to 1, ... See full document

... In 1968, Stancu introduced Bernstein-Stancu operators in [15] a linear positive opera- tor depending on two non-negative parameters a and b satisfying the condition 0 ≤ a ≤ b. Recently, many researcher applied ... See full document

... two-dimensional convective equations models (Cessi and Young, 1992; Vellinga, 1996; Lucarini et al., 2005, 2007) to simplified climate models (Stocker and Wright, 1991; Rahm- storf, 1995; Stocker and Schmittner, ... See full document

... is called the Bessel function of the index v . A large number of a wide variety of tasks related practically all the most important branches of mathematical physics and those designed to answer topical technical ... See full document

... Partial differential equations (PDE) are very important in many branches of mathematics, science and engineering such as hydrodynamics, elasticity, quantum mechanic and electromagnetic theory. In mathematics, PDE is an ... See full document

... machines, one small and one large run of PMG+PFASST is con- ducted where the small runs use a number of cores for PMG that corresponds to the point where PMG’s scaling saturates for the coarse level problem ... See full document

... In heat conduction for example, attention was paid to the unique solvability of one-dimensional inverse problems for the heat equation in the case when the unknown thermal coefficients ... See full document

... integral equations work as an important role. There are various methods such as Trapezium rule, Simpson rule, Gaussian quadrature and many others methods are exist for solving the integral equations. But these techniques ... See full document

... Convection-diffusion problems are base at modelling of problems of hydrodynamics and heat-mass transfer [2]. The basic attention at a numerical solution is given to problems of approximation of convective terms ... See full document

... two-dimensional heat transfer model of calculating temperature profile inside wax deposition layer in the flow loop experiment at a time was deduced and established by using energy balance equations, and ... See full document

... form one of the best known sys- tems of orthogonal polynomials in ...classical heat equa- tion, which is a partial differential equation involving classical ...the heat equation for ... See full document

... The shape parameter ε, which appears in tables affects both the accuracy of the esti- mate and the conditioning of the interpolation matrix [15]. Almost, for fixed values of the shape parameter ε, the condition ... See full document

... been one of the largest manufacturers of magnesium alloys for over a decade and have been a part of this larger Magnesium research project for over thirteen years ... See full document

... In the presence of several environments (or thermal baths/reservoirs) at different temperatures, the system reaches a non-equilibrium steady state where thermodynamical currents (such as heat, energy, spin, ... See full document

... The analytical solution of equation (1.1) and (1.2) were given by Fletcher. Fletcher used to the transformation Hopf- Cole [3]. Fletcher made a comparison of the different numer- ical methods [4]. Wubs and Geode ... See full document

... nonlinear one-dimensional sine-Gordon (SG) equation came into sight in the dif- ferential geometry and attracted a lot of attention because of the collisional behaviors of solitons that arise from ... See full document

... [6] q-analogue ofWhipple’s ...20 q-analogues ofthe relations between Kummer’s 24 solutions - the main results ofthis paper - are given in section ... See full document

... and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasi ´nski and Płociniczak in ... See full document

... The remainder of the paper is organized as follows: Section 2 provides a review of Hyperspace Analogue to Language, Fuzzy Logic and Fuzzy C-Means Clustering Algorithm. Section 3 describes the specifics of the ... See full document

... Analytical methods have gained the interest of researchers for finding approximate solutions to partial differential equations. This interest was driven by the needs from applications both in science and technology. ... See full document