Search results for: second-order hyperbolic telegraph equation.
1139 Septic B-spline Collocation Method for Solving One-dimensional Hyperbolic Telegraph Equation
Authors: Marzieh Dosti, Alireza Nazemi
Abstract:
Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17841138 Solving One-dimensional Hyperbolic Telegraph Equation Using Cubic B-spline Quasi-interpolation
Authors: Marzieh Dosti, Alireza Nazemi
Abstract:
In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.
Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27851137 Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation
Authors: Kew Lee Ming, Norhashidah Hj. Mohd. Ali
Abstract:
In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.Keywords: Telegraph equation, explicit group iterative scheme, domain decomposition algorithm, parallelization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15151136 Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation
Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey
Abstract:
In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13561135 A C1-Conforming Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation
Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang
Abstract:
In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.
Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18781134 Nonlinear Equations with N-dimensional Telegraph Operator Iterated K-times
Authors: Jessada Tariboon
Abstract:
In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.
Keywords: Telegraph operator, Elementary solution, Distribution kernel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11871133 An Empirical Validation of the Linear- Hyperbolic Approximation of the I-V Characteristic of a Solar Cell Generator
Authors: A. A. Penin
Abstract:
An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.
Keywords: a solar cell generator, I − V characteristic, p − n junction, approximation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14071132 On Hyperbolic Gompertz Growth Model
Authors: Angela Unna Chukwu, Samuel Oluwafemi Oyamakin
Abstract:
We proposed a Hyperbolic Gompertz Growth Model (HGGM), which was developed by introducing a shape parameter (allometric). This was achieved by convoluting hyperbolic sine function on the intrinsic rate of growth in the classical gompertz growth equation. The resulting integral solution obtained deterministically was reprogrammed into a statistical model and used in modeling the height and diameter of Pines (Pinus caribaea). Its ability in model prediction was compared with the classical gompertz growth model, an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while the independence of the error term was confirmed using the runs test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic gompertz growth models better than the source model (classical gompertz growth model) while the results of R2, Adj. R2, MSE and AIC confirmed the predictive power of the Hyperbolic Gompertz growth models over its source model.Keywords: Height, Dbh, forest, Pinus caribaea, hyperbolic, gompertz.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26941131 A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations
Authors: Jinfeng Wang, Yang Liu, Hong Li
Abstract:
In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.
Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21271130 Dynamic Variation in Nano-Scale CMOS SRAM Cells Due to LF/RTS Noise and Threshold Voltage
Authors: M. Fadlallah, G. Ghibaudo, C. G. Theodorou
Abstract:
The dynamic variation in memory devices such as the Static Random Access Memory can give errors in read or write operations. In this paper, the effect of low-frequency and random telegraph noise on the dynamic variation of one SRAM cell is detailed. The effect on circuit noise, speed, and length of time of processing is examined, using the Supply Read Retention Voltage and the Read Static Noise Margin. New test run methods are also developed. The obtained results simulation shows the importance of noise caused by dynamic variation, and the impact of Random Telegraph noise on SRAM variability is examined by evaluating the statistical distributions of Random Telegraph noise amplitude in the pull-up, pull-down. The threshold voltage mismatch between neighboring cell transistors due to intrinsic fluctuations typically contributes to larger reductions in static noise margin. Also the contribution of each of the SRAM transistor to total dynamic variation has been identified.
Keywords: Low-frequency noise, Random Telegraph Noise, Dynamic Variation, SRRV.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7061129 Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method
Authors: Anjali Verma, Ram Jiwari, Jitender Kumar
Abstract:
This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18301128 A Hyperbolic Characterization of Projective Klingenberg Planes
Authors: Basri Çelik
Abstract:
In this paper, the notion of Hyperbolic Klingenberg plane is introduced via a set of axioms like as Affine Klingenberg planes and Projective Klingenberg planes. Models of such planes are constructed by deleting a certain number m of equivalence classes of lines from a Projective Klingenberg plane. In the finite case, an upper bound for m is established and some combinatoric properties are investigated.Keywords: Hyperbolic planes, Klingenberg planes, Projective planes.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13191127 High Order Accurate Runge Kutta Nodal Discontinuous Galerkin Method for Numerical Solution of Linear Convection Equation
Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang
Abstract:
This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24611126 On Symmetry Analysis and Exact Wave Solutions of New Modified Novikov Equation
Authors: Anupma Bansal, R. K. Gupta
Abstract:
In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Keywords: New Modified Novikov Equation, Lie Classical Method, Nonclassical Method, Modified (G'/G)-Expansion Method, Traveling Wave Solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16161125 A Survey on Hyperbolic Cooling Towers
Authors: E. Asadzadeh, M. Alam
Abstract:
This study offers a comprehensive review of the research papers published in the field of cooling towers and gives an insight into the latest developments of the natural draught cooling towers. Different modeling, analysis and design techniques are summarized and the challenges are discussed. The 118 references included in this paper are mostly concentrated on the review of the published papers after 2005. The present paper represents a complete collection of the studies done for cooling towers and would give an updated material for the researchers and design engineers in the field of hyperbolic cooling towers.
Keywords: Hyperbolic cooling towers, earthquakes, wind, nonlinear behavior, buckling, collapse, interference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 39691124 Adomian Decomposition Method Associated with Boole-s Integration Rule for Goursat Problem
Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran
Abstract:
The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18451123 A Nonconforming Mixed Finite Element Method for Semilinear Pseudo-Hyperbolic Partial Integro-Differential Equations
Authors: Jingbo Yang, Hong Li, Yang Liu, Siriguleng He
Abstract:
In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.
Keywords: Pseudo-hyperbolic partial integro-differential equations, Nonconforming mixed element method, Semilinear, Error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16291122 Progressive Collapse of Hyperbolic Cooling Tower Considering the Support Inclinations
Authors: Esmaeil Asadzadeh, Mehtab Alam
Abstract:
Progressive collapse of the layered hyperbolic tower shells are studied considering the influences of changes in the supporting columns’ types and angles. 3-D time history analyses employing the finite element method are performed for the towers supported with I-type and ᴧ-type column. It is found that the inclination angle of the supporting columns is a very important parameter in optimization and safe design of the cooling towers against the progressive collapse. It is also concluded that use of Demand Capacity Ratio (DCR) criteria of the linear elastic approach recommended by GSA is un-conservative for the hyperbolic tower shells.
Keywords: Progressive collapse, cooling towers, finite element analysis, crack generation, reinforced concrete.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13461121 On Finite Hjelmslev Planes of Parameters (pk−1, p)
Authors: Atilla Akpinar
Abstract:
In this paper, we study on finite projective Hjelmslev planes M(Zq) coordinatized by Hjelmslev ring Zq (where prime power q = pk). We obtain finite hyperbolic Klingenberg planes from these planes under certain conditions. Also, we give a combinatorical result on M(Zq), related by deleting a line from lines in same neighbour.
Keywords: Finite Klingenberg plane, finite hyperbolic Klingenberg plane.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11341120 Self-Organizing Control Systems for Unstable and Deterministic Chaotic Processes
Authors: M. A. Beisenbi, N. M. Kissikova, S. E. Beisembina, S. T. Suleimenova, S. A. Kaliyeva
Abstract:
The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector-functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.
Keywords: Gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4381119 Transient Hydrodynamic and Thermal Behaviors of Fluid Flow in a Vertical Porous Microchannel under the Effect of Hyperbolic Heat Conduction Model
Authors: A. F. Khadrawi
Abstract:
The transient hydrodynamics and thermal behaviors of fluid flow in open-ended vertical parallel-plate porous microchannel are investigated semi-analytically under the effect of the hyperbolic heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The Effects of Knudsen number , Darcy number , and thermal relaxation time on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic heat conduction models. It is found that as increases the slip in the hydrodynamic and thermal boundary condition increases. This slip in the hydrodynamic boundary condition increases as increases. Also, the slip in the thermal boundary condition increases as decreases especially the early stage of time.Keywords: free convection, hyperbolic heat conduction, macroscopic heat conduction models in microchannel, porous media, vertical microchannel, microchannel thermal, hydrodynamic behavior.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19171118 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t
Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim
Abstract:
Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.
Keywords: Pell equation, Diophantine equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23691117 Iteration Acceleration for Nonlinear Coupled Parabolic-Hyperbolic System
Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue
Abstract:
A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.
Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15491116 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4
Authors: Armend Sh. Shabani
Abstract:
Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan.Keywords: Pell's equation, solutions of Pell's equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12221115 Affine Radial Basis Function Neural Networks for the Robust Control of Hyperbolic Distributed Parameter Systems
Authors: Eleni Aggelogiannaki, Haralambos Sarimveis
Abstract:
In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.
Keywords: Hyperbolic Distributed Parameter Systems, Radial Basis Function Neural Networks, H∞ control, Thermal systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14081114 A Nano-Scaled SRAM Guard Band Design with Gaussian Mixtures Model of Complex Long Tail RTN Distributions
Authors: Worawit Somha, Hiroyuki Yamauchi
Abstract:
This paper proposes, for the first time, how the challenges facing the guard-band designs including the margin assist-circuits scheme for the screening-test in the coming process generations should be addressed. The increased screening error impacts are discussed based on the proposed statistical analysis models. It has been shown that the yield-loss caused by the misjudgment on the screening test would become 5-orders of magnitude larger than that for the conventional one when the amplitude of random telegraph noise (RTN) caused variations approaches to that of random dopant fluctuation. Three fitting methods to approximate the RTN caused complex Gamma mixtures distributions by the simple Gaussian mixtures model (GMM) are proposed and compared. It has been verified that the proposed methods can reduce the error of the fail-bit predictions by 4-orders of magnitude.Keywords: Mixtures of Gaussian, Random telegraph noise, EM algorithm, Long-tail distribution, Fail-bit analysis, Static random access memory, Guard band design.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18341113 The Hyperbolic Smoothing Approach for Automatic Calibration of Rainfall-Runoff Models
Authors: Adilson Elias Xavier, Otto Corrêa Rotunno Filho, Paulo Canedo de Magalhães
Abstract:
This paper addresses the issue of automatic parameter estimation in conceptual rainfall-runoff (CRR) models. Due to threshold structures commonly occurring in CRR models, the associated mathematical optimization problems have the significant characteristic of being strongly non-differentiable. In order to face this enormous task, the resolution method proposed adopts a smoothing strategy using a special C∞ differentiable class function. The final estimation solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original conceptual problem. The use of this technique, called Hyperbolic Smoothing Method (HSM), makes possible the application of the most powerful minimization algorithms, and also allows for the main difficulties presented by the original CRR problem to be overcome. A set of computational experiments is presented for the purpose of illustrating both the reliability and the efficiency of the proposed approach.
Keywords: Rainfall-runoff models, optimization procedure, automatic parameter calibration, hyperbolic smoothing method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3961112 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
Abstract:
In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20091111 The Pell Equation x2 − Py2 = Q
Authors: Ahmet Tekcan, Arzu Özkoç, Canan Kocapınar, Hatice Alkan
Abstract:
Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.Keywords: Pell equation, solutions of Pell equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20931110 MHD Natural Convection Flow of Tangent Hyperbolic Nanofluid Past a Vertical Permeable Cone
Authors: A. Mahdy
Abstract:
In this paper, a non-similraity analysis has been presented to exhibit the two-dimensional boundary layer flow of magnetohydrodynamic (MHD) natural convection of tangent hyperbolic nanofluid nearby a vertical permeable cone in the presence of variable wall temperature impact. The mutated boundary layer nonlinear governing equations are solved numerically by the an efficient implicit finite difference procedure. For both nanofluid effective viscosity and nanofluid thermal conductivity, a number of experimental relations have been recognized. For characterizing the nanofluid, the compatible nanoparticle volume fraction model has been used. Nusselt number and skin friction coefficient are calculated for some values of Weissenberg number W, surface temperature exponent n, magnetic field parameter Mg, power law index m and Prandtl number Pr as functions of suction parameter. The rate of heat transfer from a vertical permeable cone in a regular fluid is less than that in nanofluids. A best convection has been presented by Copper nanoparticle among all the used nanoparticles.Keywords: Tangent hyperbolic nanofluid, finite difference, non-similarity, isothermal cone.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 772