**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**654

# Search results for: Linear Differential Inclusion

##### 654 Two-dimensional Differential Transform Method for Solving Linear and Non-linear Goursat Problem

**Authors:**
H. Taghvafard,
G. H. Erjaee

**Abstract:**

**Keywords:**
Quadrature,
Spline interpolation,
Trapezoidal rule,
Numericalintegration,
Error analysis.

##### 653 The Differential Transform Method for Advection-Diffusion Problems

**Authors:**
M. F. Patricio,
P. M. Rosa

**Abstract:**

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

**Keywords:**
Method of Lines,
Differential Transform Method.

##### 652 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach

**Authors:**
Lianglin Xiong,
Yun Zhao,
Tao Jiang

**Abstract:**

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

**Keywords:**
Fractional neutral differential equation,
Laplace transform,
characteristic equation.

##### 651 2 – Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations

**Authors:**
Abdu Masanawa Sagir

**Abstract:**

**Keywords:**
Block Method,
Hybrid,
Linear Multistep Method,
Self – starting,
Special Second Order.

##### 650 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations

**Authors:**
Sara Barati,
Karim Ivaz

**Abstract:**

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

**Keywords:**
Variational iteration method,
delay differential equations,
multiple delays,
Runge-Kutta method.

##### 649 Optimal Control of a Linear Distributed Parameter System via Shifted Legendre Polynomials

**Authors:**
Sanjeeb Kumar Kar

**Abstract:**

**Keywords:**
Optimal control,
linear systems,
distributed parametersystems,
Legendre polynomials.

##### 648 ψ-exponential Stability for Non-linear Impulsive Differential Equations

**Authors:**
Bhanu Gupta,
Sanjay K. Srivastava

**Abstract:**

**Keywords:**
Exponential stability,
globally exponential stability,
impulsive differential equations,
Lyapunov function,
ψ-stability.

##### 647 Projective Synchronization of a Class of Fractional-Order Chaotic Systems

**Authors:**
Zahra Yaghoubi,
Nooshin Bigdeli,
Karim Afshar

**Abstract:**

##### 646 Delay-independent Stabilization of Linear Systems with Multiple Time-delays

**Authors:**
Ping He,
Heng-You Lan,
Gong-Quan Tan

**Abstract:**

**Keywords:**
Linear system,
Delay-independent stabilization,
Lyapunovfunctional,
Riccati algebra matrix equation.

##### 645 Numerical Algorithms for Solving a Type of Nonlinear Integro-Differential Equations

**Authors:**
Shishen Xie

**Abstract:**

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

**Keywords:**
variation iteration method,
decomposition method,
nonlinear integro-differential equations

##### 644 Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type

**Authors:**
Kazuo Komatsu,
Hitoshi Takata

**Abstract:**

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

**Keywords:**
nonlinear system,
augmented linear system,
nonlinear observer,
formal linearization,
electric power system.

##### 643 Signal Transmission Analysis of Differential Pairs Using Semicircle-Shaped Via Structure

**Authors:**
Moonjung Kim,
Chang-Ho Hyun,
Won-Ho Kim

**Abstract:**

**Keywords:**
Differential pairs,
signal transmission property,
via,
S-parameter.

##### 642 Blow up in Polynomial Differential Equations

**Authors:**
Rudolf Csikja,
Janos Toth

**Abstract:**

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

**Keywords:**
blow up,
finite escape time,
polynomial ODE,
singularity,
Lotka–Volterra equation,
Painleve analysis,
Ψ-series,
global existence

##### 641 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

**Authors:**
Tarun Kumar Rawat,
Abhirup Lahiri,
Ashish Gupta

**Abstract:**

In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.

**Keywords:**
Single-ended input differential amplifier,
Noise,
stochastic differential equation,
mean and variance.

##### 640 A Sandwich-type Theorem with Applications to Univalent Functions

**Authors:**
Sukhwinder Singh Billing,
Sushma Gupta,
Sukhjit Singh Dhaliwal

**Abstract:**

**Keywords:**
Univalent function,
Starlike function,
Differential subordination,
Differential superordination.

##### 639 Evolutionary Computation Technique for Solving Riccati Differential Equation of Arbitrary Order

**Authors:**
Raja Muhammad Asif Zahoor,
Junaid Ali Khan,
I. M. Qureshi

**Abstract:**

**Keywords:**
Riccati Equation,
Non linear ODE,
Fractional differential equation,
Genetic algorithm.

##### 638 Numerical Simulation of unsteady MHD Flow and Heat Transfer of a Second Grade Fluid with Viscous Dissipation and Joule Heating using Meshfree Approach

**Authors:**
R. Bhargava,
Sonam Singh

**Abstract:**

**Keywords:**
EFGM,
MHD,
Oscillatory stretching sheet,
Unsteady,
Viscoelastic

##### 637 Solving of the Fourth Order Differential Equations with the Neumann Problem

**Authors:**
Marziyeh Halimi,
Roushanak Lotfikar,
Simin Mansouri Borojeni

**Abstract:**

**Keywords:**
Neumann problem,
weighted Sobolev spaces,
generalized solution,
spectrum of linear operators.2000 mathematic subject classification: 34A05,
34A30.

##### 636 Dynamic Modeling and Simulation of Heavy Paraffin Dehydrogenation Reactor for Selective Olefin Production in Linear Alkyl Benzene Production Plant

**Authors:**
G. Zahedi,
H. Yaghoobi

**Abstract:**

**Keywords:**
Dehydrogenation,
fixed bed reactor,
modeling,
linear alkyl benzene.

##### 635 Prediction of the Total Decay Heat from Fast Neutron Fission of 235U and 239Pu

**Authors:**
Sherif. S. Nafee,
Ameer. K. Al-Ramady,
Salem. A. Shaheen

**Abstract:**

**Keywords:**
Decay heat,
fast neutron fission,
and Numerical Solution of Linear Differential Equations.

##### 634 Linear-Operator Formalism in the Analysis of Omega Planar Layered Waveguides

**Authors:**
António L. Topa

**Abstract:**

**Keywords:**
Metamaterials,
linear operators,
omega media,
layered waveguide,
orthogonality relations

##### 633 Simplex Method for Fuzzy Variable Linear Programming Problems

**Authors:**
S.H. Nasseri,
E. Ardil

**Abstract:**

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

**Keywords:**
Fuzzy variable linear programming,
fuzzy number,
ranking function,
simplex method.

##### 632 Decay Heat Contribution Analyses of Curium Isotopes in the Mixed Oxide Nuclear Fuel

**Authors:**
S. S. Nafee,
A. K. Al-Ramady,
S. A. Shaheen

**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.

**Keywords:**
Decay heat,
Mixed oxide nuclear fuel,
Numerical
Solution of Linear Differential Equations,
and Curium isotopes

##### 631 Estimating Reaction Rate Constants with Neural Networks

**Authors:**
Benedek Kovacs,
Janos Toth

**Abstract:**

Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.

**Keywords:**
Neural networks,
parameter estimation,
linear regression,
kinetic models,
reaction rate coefficients.

##### 630 Existence of Solution for Boundary Value Problems of Differential Equations with Delay

**Authors:**
Xiguang Li

**Abstract:**

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

**Keywords:**
Banach space,
boundary value problem,
differential equation,
delay.

##### 629 Modeling Approaches for Large-Scale Reconfigurable Engineering Systems

**Authors:**
Kwa-Sur Tam

**Abstract:**

**Keywords:**
Interdisciplinary,
dynamic,
functional programming,
object-oriented.

##### 628 Exterior Calculus: Economic Growth Dynamics

**Authors:**
Troy L. Story

**Abstract:**

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

**Keywords:**
Differential geometry,
exterior calculus,
Hamiltonian geometry,
mathematical economics.

##### 627 Exterior Calculus: Economic Profit Dynamics

**Authors:**
Troy L. Story

**Abstract:**

**Keywords:**
Differential geometry,
exterior calculus,
Hamiltonian
geometry,
mathematical economics,
economic functions,
and
dynamics

##### 626 Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations

**Authors:**
Khairil Iskandar Othman,
Zarina Bibi Ibrahim,
Mohamed Suleiman

**Abstract:**

**Keywords:**
Backward Differentiation Formula,
block,
ordinarydifferential equations.

##### 625 Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers

**Authors:**
S. H. Nasseri,
E. Ardil,
A. Yazdani,
R. Zaefarian

**Abstract:**

**Keywords:**
Fuzzy number linear programming,
rankingfunction,
simplex method.