**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1139

# 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.

##### 1138 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.

##### 1137 Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation

**Authors:**
Kew Lee Ming,
Norhashidah Hj. Mohd. Ali

**Abstract:**

**Keywords:**
Telegraph equation,
explicit group iterative scheme,
domain decomposition algorithm,
parallelization.

##### 1136 Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation

**Authors:**
Anupma Bansal,
Rajeev Budhiraja,
Manoj Pandey

**Abstract:**

**Keywords:**
Nonlinear time-fractional hyperbolic PDE,
Lie
Classical method,
exact solutions.

##### 1135 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.

##### 1134 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.

##### 1133 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

##### 1132 On Hyperbolic Gompertz Growth Model

**Authors:**
Angela Unna Chukwu,
Samuel Oluwafemi Oyamakin

**Abstract:**

**Keywords:**
Height,
Dbh,
forest,
Pinus caribaea,
hyperbolic,
gompertz.

##### 1131 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

##### 1130 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.

##### 1129 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.

##### 1128 A Hyperbolic Characterization of Projective Klingenberg Planes

**Authors:**
Basri Çelik

**Abstract:**

**Keywords:**
Hyperbolic planes,
Klingenberg planes,
Projective
planes.

##### 1127 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:**

**Keywords:**
Nodal Discontinuous Galerkin Method,
RKDG,
Scalar Wave Equation,
LSERK

##### 1126 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.

##### 1125 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.

##### 1124 Adomian Decomposition Method Associated with Boole-s Integration Rule for Goursat Problem

**Authors:**
Mohd Agos Salim Nasir,
Ros Fadilah Deraman,
Siti Salmah Yasiran

**Abstract:**

**Keywords:**
Goursat problem,
partial differential equation,
Adomian decomposition method,
Boole's integration rule.

##### 1123 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.

##### 1122 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.

##### 1121 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.

##### 1120 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.

##### 1119 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:**

**Keywords:**
free convection,
hyperbolic heat conduction,
macroscopic heat conduction models in microchannel,
porous media,
vertical microchannel,
microchannel thermal,
hydrodynamic behavior.

##### 1118 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.

##### 1117 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.

##### 1116 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.

##### 1115 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 1114 A Nano-Scaled SRAM Guard Band Design with Gaussian Mixtures Model of Complex Long Tail RTN Distributions

**Authors:**
Worawit Somha,
Hiroyuki Yamauchi

**Abstract:**

**Keywords:**
Mixtures of Gaussian,
Random telegraph noise,
EM
algorithm,
Long-tail distribution,
Fail-bit analysis,
Static random
access memory,
Guard band design.

##### 1113 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.

##### 1112 MHD Natural Convection Flow of Tangent Hyperbolic Nanofluid Past a Vertical Permeable Cone

**Authors:**
A. Mahdy

**Abstract:**

**Keywords:**
Tangent hyperbolic nanofluid,
finite difference,
non-similarity,
isothermal cone.

##### 1111 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.

##### 1110 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.