Abstract: In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.
Abstract: the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction
Abstract: Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.
Abstract: Taking into account that many problems of natural
sciences and engineering are reduced to solving initial-value problem
for ordinary differential equations, beginning from Newton, the
scientists investigate approximate solution of ordinary differential
equations. There are papers of different authors devoted to the
solution of initial value problem for ODE. The Euler-s known
method that was developed under the guidance of the famous
scientists Adams, Runge and Kutta is the most popular one among
these methods.
Recently the scientists began to construct the methods preserving
some properties of Adams and Runge-Kutta methods and called them
hybrid methods. The constructions of such methods are investigated
from the middle of the XX century. Here we investigate one
generalization of multistep and hybrid methods and on their base we
construct specific methods of accuracy order p = 5 and p = 6 for
k = 1 ( k is the order of the difference method).
Abstract: In this paper, a new learning algorithm based on a
hybrid metaheuristic integrating Differential Evolution (DE) and
Reduced Variable Neighborhood Search (RVNS) is introduced to train
the classification method PROAFTN. To apply PROAFTN, values of
several parameters need to be determined prior to classification. These
parameters include boundaries of intervals and relative weights for
each attribute. Based on these requirements, the hybrid approach,
named DEPRO-RVNS, is presented in this study. In some cases, the
major problem when applying DE to some classification problems
was the premature convergence of some individuals to local optima.
To eliminate this shortcoming and to improve the exploration and
exploitation capabilities of DE, such individuals were set to iteratively
re-explored using RVNS. Based on the generated results on
both training and testing data, it is shown that the performance of
PROAFTN is significantly improved. Furthermore, the experimental
study shows that DEPRO-RVNS outperforms well-known machine
learning classifiers in a variety of problems.
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.
Abstract: A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.
Abstract: The paper aims at investigating influence of medium
capacity on linear adsorbed solute dispersion into chemically
heterogeneous fixed beds. A discrete chemical heterogeneity
distribution is considered in the one-dimensional advectivedispersive
equation. The partial differential equation is solved using
finite volumes method based on the Adam-Bashforth algorithm.
Increased dispersion is estimated by comparing breakthrough curves
second order moments and keeping identical hydrodynamic
properties. As a result, dispersion increase due to chemical
heterogeneity depends on the column size and surprisingly on the
solid capacity. The more intense capacity is, the more important
solute dispersion is. Medium length which is known to favour this
effect vanishing according to the linear adsorption in fixed bed seems
to create nonmonotonous variation of dispersion because of the
heterogeneity. This nonmonotonous behaviour is also favoured by
high capacities.
Abstract: Orthogonal Frequency Division Multiplexing (OFDM) is one of the techniques for high speed data rate communication with main consideration for 4G and 5G systems. In OFDM, there are several mapping schemes which provide a way of parallel transmission. In this paper, comparisons of mapping schemes used by some standards have been made and also has been discussed about the performance of the non-conventional modulation technique. The Comparisons of Bit Error Rate (BER) performances for conventional and non-conventional modulation schemes have been done using MATLAB software. Mentioned schemes used in OFDM system can be selected on the basis of the requirement of power or spectrum efficiency and BER analysis.
Abstract: A nonlinear model of two-beam free-electron laser
(FEL) in the absence of slippage is presented. The two beams are
assumed to be cold with different energies and the fundamental
resonance of the higher energy beam is at the third harmonic of lower
energy beam. By using Maxwell-s equations and full Lorentz force
equations of motion for the electron beams, coupled differential
equations are derived and solved numerically by the fourth order
Runge–Kutta method. In this method a considerable growth of third
harmonic electromagnetic field in the XUV and X-ray regions is
predicted.
Abstract: The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.
Abstract: This paper proposes a low-voltage and low-power
fully integrated digitally tuned continuous-time channel selection
filter for WiMAX applications. A 5th-order elliptic low-pass filter is
realized in a Gm-C topology. The bandwidth of the fully differential
filter is reconfigurable from 2.5MHz to 20MHz (8x) for different
requirements in WiMAX applications. The filter is simulated in a
standard 90nm CMOS process. Simulation results show the THD
(@Vout =100mVpp) is less than -66dB. The in-band ripple of the
filter is about 0.15dB. The filter consumes 1.5mW from a supply
voltage of 0.9V.
Abstract: In this paper, solution of fuzzy differential equation
under general differentiability is obtained by simulink. The simulink
solution is equivalent or very close to the exact solution of the
problem. Accuracy of the simulink solution to this problem is
qualitatively better. An illustrative numerical example is presented
for the proposed method.
Abstract: This paper addresses the problem of asymptotic tracking
control of a linear parabolic partial differential equation with indomain
point actuation. As the considered model is a non-standard
partial differential equation, we firstly developed a map that allows
transforming this problem into a standard boundary control problem
to which existing infinite-dimensional system control methods can
be applied. Then, a combination of energy multiplier and differential
flatness methods is used to design an asymptotic tracking controller.
This control scheme consists of stabilizing state-feedback derived
from the energy multiplier method and feed-forward control based
on the flatness property of the system. This approach represents
a systematic procedure to design tracking control laws for a class
of partial differential equations with in-domain point actuation. The
applicability and system performance are assessed by simulation
studies.
Abstract: The motion of a sphere moving along the axis of a
rotating viscous fluid is studied at high Reynolds numbers and
moderate values of Taylor number. The Higher Order Compact
Scheme is used to solve the governing Navier-Stokes equations. The
equations are written in the form of Stream function, Vorticity
function and angular velocity which are highly non-linear, coupled
and elliptic partial differential equations. The flow is governed by
two parameters Reynolds number (Re) and Taylor number (T). For
very low values of Re and T, the results agree with the available
experimental and theoretical results in the literature. The results are
obtained at higher values of Re and moderate values of T and
compared with the experimental results. The results are fourth order
accurate.
Abstract: The aim of this paper is to investigate the
performance of the developed two point block method designed for
two processors for solving directly non stiff large systems of higher
order ordinary differential equations (ODEs). The method calculates
the numerical solution at two points simultaneously and produces
two new equally spaced solution values within a block and it is
possible to assign the computational tasks at each time step to a
single processor. The algorithm of the method was developed in C
language and the parallel computation was done on a parallel shared
memory environment. Numerical results are given to compare the
efficiency of the developed method to the sequential timing. For
large problems, the parallel implementation produced 1.95 speed-up
and 98% efficiency for the two processors.
Abstract: In this paper, a new approach is introduced to solve
Blasius equation using parameter identification of a nonlinear
function which is used as approximation function. Bees Algorithm
(BA) is applied in order to find the adjustable parameters of
approximation function regarding minimizing a fitness function
including these parameters (i.e. adjustable parameters). These
parameters are determined how the approximation function has to
satisfy the boundary conditions. In order to demonstrate the
presented method, the obtained results are compared with another
numerical method. Present method can be easily extended to solve a
wide range of problems.
Abstract: Einstein vacuum equations, that is a system of nonlinear
partial differential equations (PDEs) are derived from Weyl metric
by using relation between Einstein tensor and metric tensor. The
symmetries of Einstein vacuum equations for static axisymmetric
gravitational fields are obtained using the Lie classical method. We
have examined the optimal system of vector fields which is further
used to reduce nonlinear PDE to nonlinear ordinary differential
equation (ODE). Some exact solutions of Einstein vacuum equations
in general relativity are also obtained.
Abstract: Masonry cavity walls are loaded by wind pressure and vertical load from upper floors. These loads results in bending moments and compression forces in the ties connecting the outer and the inner wall in a cavity wall. Large cavity walls are furthermore loaded by differential movements from the temperature gradient between the outer and the inner wall, which results in critical increase of the bending moments in the ties. Since the ties are loaded by combined compression and moment forces, the loadbearing capacity is derived from instability equilibrium equations. Most of them are iterative, since exact instability solutions are complex to derive, not to mention the extra complexity introducing dimensional instability from the temperature gradients. Using an inverse variable substitution and comparing an exact theory with an analytical instability solution a method to design tie-connectors in cavity walls was developed. The method takes into account constraint conditions limiting the free length of the wall tie, and the instability in case of pure compression which gives an optimal load bearing capacity. The model is illustrated with examples from praxis.
Abstract: The simulation of extrusion process is studied widely
in order to both increase products and improve quality, with broad
application in wire coating. The annular tube-tooling extrusion was
set up by a model that is termed as Navier-Stokes equation in
addition to a rheological model of differential form based on singlemode
exponential Phan-Thien/Tanner constitutive equation in a twodimensional
cylindrical coordinate system for predicting the
contraction point of the polymer melt beyond the die. Numerical
solutions are sought through semi-implicit Taylor-Galerkin pressurecorrection
finite element scheme. The investigation was focused on
incompressible creeping flow with long relaxation time in terms of
Weissenberg numbers up to 200. The isothermal case was considered
with surface tension effect on free surface in extrudate flow and no
slip at die wall. The Stream Line Upwind Petrov-Galerkin has been
proposed to stabilize solution. The structure of mesh after die exit
was adjusted following prediction of both top and bottom free
surfaces so as to keep the location of contraction point around one
unit length which is close to experimental results. The simulation of
extrusion process is studied widely in order to both increase products
and improve quality, with broad application in wire coating. The
annular tube-tooling extrusion was set up by a model that is termed
as Navier-Stokes equation in addition to a rheological model of
differential form based on single-mode exponential Phan-
Thien/Tanner constitutive equation in a two-dimensional cylindrical
coordinate system for predicting the contraction point of the polymer
melt beyond the die. Numerical solutions are sought through semiimplicit
Taylor-Galerkin pressure-correction finite element scheme.
The investigation was focused on incompressible creeping flow with
long relaxation time in terms of Weissenberg numbers up to 200. The
isothermal case was considered with surface tension effect on free
surface in extrudate flow and no slip at die wall. The Stream Line
Upwind Petrov-Galerkin has been proposed to stabilize solution. The
structure of mesh after die exit was adjusted following prediction of
both top and bottom free surfaces so as to keep the location of
contraction point around one unit length which is close to
experimental results.