Abstract: In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).
Abstract: Wavelet transform or wavelet analysis is a recently
developed mathematical tool in applied mathematics. In numerical
analysis, wavelets also serve as a Galerkin basis to solve partial
differential equations. Haar transform or Haar wavelet transform has
been used as a simplest and earliest example for orthonormal wavelet
transform. Since its popularity in wavelet analysis, there are several
definitions and various generalizations or algorithms for calculating
Haar transform. Fast Haar transform, FHT, is one of the algorithms
which can reduce the tedious calculation works in Haar transform. In
this paper, we present a modified fast and exact algorithm for FHT,
namely Modified Fast Haar Transform, MFHT. The algorithm or
procedure proposed allows certain calculation in the process
decomposition be ignored without affecting the results.
Abstract: The multidelays linear control systems described by
difference differential equations are often studied in modern control
theory. In this paper, the delay-independent stabilization algebraic
criteria and the theorem of delay-independent stabilization for linear
systems with multiple time-delays are established by using the
Lyapunov functional and the Riccati algebra matrix equation in the
matrix theory. An illustrative example and the simulation result, show
that the approach to linear systems with multiple time-delays is
effective.
Abstract: A novel PDE solver using the multidimensional wave
digital filtering (MDWDF) technique to achieve the solution of a 2D
seismic wave system is presented. In essence, the continuous physical
system served by a linear Kirchhoff circuit is transformed to an
equivalent discrete dynamic system implemented by a MD wave
digital filtering (MDWDF) circuit. This amounts to numerically
approximating the differential equations used to describe elements of a
MD passive electronic circuit by a grid-based difference equations
implemented by the so-called state quantities within the passive
MDWDF circuit. So the digital model can track the wave field on a
dense 3D grid of points. Details about how to transform the continuous
system into a desired discrete passive system are addressed. In
addition, initial and boundary conditions are properly embedded into
the MDWDF circuit in terms of state quantities. Graphic results have
clearly demonstrated some physical effects of seismic wave (P-wave
and S–wave) propagation including radiation, reflection, and
refraction from and across the hard boundaries. Comparison between
the MDWDF technique and the finite difference time domain (FDTD)
approach is also made in terms of the computational efficiency.
Abstract: In this paper zero-dissipative explicit Runge-Kutta
method is derived for solving second-order ordinary differential
equations with periodical solutions. The phase-lag and dissipation
properties for Runge-Kutta (RK) method are also discussed. The new
method has algebraic order three with dissipation of order infinity.
The numerical results for the new method are compared with existing
method when solving the second-order differential equations with
periodic solutions using constant step size.
Abstract: This paper considers the effect of heat generation
proportional l to (T - T∞ )p , where T is the local temperature and T∞
is the ambient temperature, in unsteady free convection flow near the
stagnation point region of a three-dimensional body. The fluid is
considered in an ambient fluid under the assumption of a step change
in the surface temperature of the body. The non-linear coupled partial
differential equations governing the free convection flow are solved
numerically using an implicit finite-difference method for different
values of the governing parameters entering these equations. The
results for the flow and heat characteristics when p ≤ 2 show that
the transition from the initial unsteady-state flow to the final steadystate
flow takes place smoothly. The behavior of the flow is seen
strongly depend on the exponent p.
Abstract: The mixed oxide nuclear fuel (MOX) of U and Pu contains several percent of fission products and minor actinides, such as neptunium, americium and curium. It is important to determine accurately the decay heat from Curium isotopes as they contribute significantly in the MOX fuel. This heat generation can cause samples to melt very quickly if excessive quantities of curium are present. In the present paper, we introduce a new approach that can predict the decay heat from curium isotopes. This work is a part of the project funded by King Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, and take place in King Abdulaziz University (KAU), Saudi Arabia. The approach is based on the numerical solution of coupled linear differential equations that describe decays and buildups of many nuclides to calculate the decay heat produced after shutdown. Results show the consistency and reliability of the approach applied.
Abstract: The objectif of the present work is to determinate the
potential of the solar parabolic trough collector (PTC) for use in the
design of a solar thermal power plant in Algeria. The study is based
on a mathematical modeling of the PTC. Heat balance has been
established respectively on the heat transfer fluid (HTF), the absorber
tube and the glass envelop using the principle of energy conservation
at each surface of the HCE cross-sectionn. The modified Euler
method is used to solve the obtained differential equations. At first
the results for typical days of two seasons the thermal behavior of the
HTF, the absorber and the envelope are obtained. Then to determine
the thermal performances of the heat transfer fluid, different oils are
considered and their temperature and heat gain evolutions compared.
Abstract: In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.
Abstract: Unsteady magnetohydrodynamics (MHD) boundary
layer flow and heat transfer over a continuously stretching surface in
the presence of radiation is examined. By similarity transformation,
the governing partial differential equations are transformed to a set of
ordinary differential equations. Numerical solutions are obtained by
employing the Runge-Kutta-Fehlberg method scheme with shooting
technique in Maple software environment. The effects of
unsteadiness parameter, radiation parameter, magnetic parameter and
Prandtl number on the heat transfer characteristics are obtained and
discussed. It is found that the heat transfer rate at the surface
increases as the Prandtl number and unsteadiness parameter increase
but decreases with magnetic and radiation parameter.
Abstract: In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.
Abstract: In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.
Abstract: The analytical prediction of the decay heat results
from the fast neutron fission of actinides was initiated under a project, 10-MAT1134-3, funded by king Abdulaziz City of Science
and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, managed by a team
from King Abdulaziz University (KAU), Saudi Arabia, and
supervised by Argonne National Laboratory (ANL) has collaborated
with KAU's team to assist in the computational analysis. In this paper, the numerical solution of coupled linear differential equations
that describe the decays and buildups of minor fission product MFA, has been used to predict the total decay heat and its components from the fast neutron fission of 235U and 239Pu. The reliability of the present approach is illustrated via systematic
comparisons with the measurements reported by the University of
Tokyo, in YAYOI reactor.
Abstract: The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.
Abstract: In this paper, we shall present sufficient conditions
for the ψ-exponential stability of a class of nonlinear impulsive
differential equations. We use the Lyapunov method with functions
that are not necessarily differentiable. In the last section, we give
some examples to support our theoretical results.
Abstract: In the paper the mathematical model of tumor
growth is considered. New capillary network formation,
which supply cancer cells with the nutrients, is taken into the
account. A formula estimating a tumor growth in connection
with the number of capillaries is obtained.
Abstract: The optimal control problem of a linear distributed
parameter system is studied via shifted Legendre polynomials (SLPs)
in this paper. The partial differential equation, representing the
linear distributed parameter system, is decomposed into an n - set
of ordinary differential equations, the optimal control problem is
transformed into a two-point boundary value problem, and the twopoint
boundary value problem is reduced to an initial value problem
by using SLPs. A recursive algorithm for evaluating optimal control
input and output trajectory is developed. The proposed algorithm is
computationally simple. An illustrative example is given to show the
simplicity of the proposed approach.
Abstract: In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.
Abstract: The subcellular organelles called oil bodies (OBs) are lipid-filled quasi-spherical droplets produced from the endoplasmic reticulum (ER) and then released into the cytoplasm during seed development. It is believed that an OB grows by coalescence with other OBs and that its stability depends on the composition of oleosins, major proteins inserted in the hemi membrane that covers OBs. In this study, we measured the OB-volume distribution from different genotypes of A. thaliana after 7, 8, 9, 10 and 11 days of seed development. In order to test the hypothesis of OBs dynamics, we developed a simple mathematical model using non-linear differential equations inspired from the theory of coagulation. The model describes the evolution of OB-volume distribution during the first steps of seed development by taking into consideration the production of OBs, the increase of triacylglycerol volume to be stored, and the growth by coalescence of OBs. Fitted parameters values show an increase in the OB production and coalescence rates in A. thaliana oleosin mutants compared to wild type.
Abstract: Modeling of a heterogeneous industrial fixed bed
reactor for selective dehydrogenation of heavy paraffin with Pt-Sn-
Al2O3 catalyst has been the subject of current study. By applying
mass balance, momentum balance for appropriate element of reactor
and using pressure drop, rate and deactivation equations, a detailed
model of the reactor has been obtained. Mass balance equations have
been written for five different components. In order to estimate
reactor production by the passage of time, the reactor model which is
a set of partial differential equations, ordinary differential equations
and algebraic equations has been solved numerically.
Paraffins, olefins, dienes, aromatics and hydrogen mole percent as
a function of time and reactor radius have been found by numerical
solution of the model. Results of model have been compared with
industrial reactor data at different operation times. The comparison
successfully confirms validity of proposed model.