**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1765

# Search results for: Linear Multistep

##### 1765 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

**Authors:**
A. A. James,
A. O. Adesanya,
M. R. Odekunle,
D. G. Yakubu

**Abstract:**

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

**Keywords:**
Interpolation,
Approximate Solution,
Collocation,
Differential system,
Half step,
Converges,
Block method,
Efficiency.

##### 1764 A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations

**Authors:**
A. M. Sagir

**Abstract:**

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

##### 1763 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.

##### 1762 Research of a Multistep Method Applied to Numerical Solution of Volterra Integro-Differential Equation

**Authors:**
M.Imanova,
G.Mehdiyeva,
V.Ibrahimov

**Abstract:**

**Keywords:**
Volterra integro-differential equations,
multistepmethods,
finite-difference methods,
initial value problem

##### 1761 On a Way for Constructing Numerical Methods on the Joint of Multistep and Hybrid Methods

**Authors:**
G.Mehdiyeva,
M.Imanova,
V.Ibrahimov

**Abstract:**

**Keywords:**
Multistep and hybrid methods,
initial value problem,
degree and stability of hybrid methods

##### 1760 An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations

**Authors:**
Gholamreza Hojjati,
Kourosh Parand

**Abstract:**

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

**Keywords:**
Lane-Emden type equations,
nonlinear ODE,
stiff problems,
multistep methods,
astrophysics.

##### 1759 Reducing Uncertainty of Monte Carlo Estimated Fatigue Damage in Offshore Wind Turbines Using FORM

**Authors:**
Jan-Tore H. Horn,
Jørgen Juncher Jensen

**Abstract:**

**Keywords:**
Fatigue damage,
FORM,
monopile,
monte carlo
simulation,
reliability,
wind turbine.

##### 1758 A Comparison of the Sum of Squares in Linear and Partial Linear Regression Models

**Authors:**
Dursun Aydın

**Abstract:**

**Keywords:**
Partial Linear Regression Model,
Linear RegressionModel,
Residuals,
Deviance,
Smoothing Spline.

##### 1757 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations

**Authors:**
A. M. Sagir

**Abstract:**

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y_{0}, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

**Keywords:**
Block Method,
Hybrid,
Linear Multistep,
Self starting,
Third Order Ordinary Differential Equations.

##### 1756 Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations

**Authors:**
A. M. Sagir

**Abstract:**

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

**Keywords:**
Block Method,
First Order Ordinary Differential Equations,
Hybrid,
Self starting.

##### 1755 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.

##### 1754 An Accurate Computation of Block Hybrid Method for Solving Stiff Ordinary Differential Equations

**Authors:**
A. M. Sagir

**Abstract:**

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

##### 1753 Bi-linear Complementarity Problem

**Authors:**
Chao Wang,
Ting-Zhu Huang Chen Jia

**Abstract:**

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

**Keywords:**
Bi-linear complementarity problem,
Linear complementarity
problem,
Extended linear complementarity problem,
Error
estimation,
P-matrix,
M-matrix.

##### 1752 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.

##### 1751 A CTL Specification of Serializability for Transactions Accessing Uniform Data

**Authors:**
Rafat Alshorman,
Walter Hussak

**Abstract:**

**Keywords:**
computational tree logic,
serializability,
multi-step
transactions.

##### 1750 Modified Buck Boost Circuit for Linear and Non-Linear Piezoelectric Energy Harvesting

**Authors:**
I Made Darmayuda,
Chai Tshun Chuan Kevin,
Je Minkyu

**Abstract:**

Plenty researches have reported techniques to harvest energy from piezoelectric transducer. In the earlier years, the researches mainly report linear energy harvesting techniques whereby interface circuitry is designed to have input impedance that match with the impedance of the piezoelectric transducer. In recent years non-linear techniques become more popular. The non-linear technique employs voltage waveform manipulation to boost the available-for-extraction energy at the time of energy transfer. The fact that non-linear energy extraction provides larger available-for-extraction energy doesn’t mean the linear energy extraction is completely obsolete. In some scenarios, such as where initial power is not available, linear energy extraction is still preferred. A modified Buck Boost circuit which is capable of harvesting piezoelectric energy using both linear and non-linear techniques is reported in this paper. Efficiency of at least 64% can be achieved using this circuit. For linear extraction, the modified Buck Boost circuit is controlled using a fix frequency and duty cycle clock. A voltage sensor and a pulse generator are added as the controller for the non-linear extraction technique.

**Keywords:**
Buck boost,
energy harvester,
linear energy harvester,
non-linear energy harvester,
piezoelectric,
synchronized charge extraction.

##### 1749 The Relative Efficiency of Parameter Estimation in Linear Weighted Regression

**Authors:**
Baoguang Tian,
Nan Chen

**Abstract:**

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

**Keywords:**
Linear weighted regression,
Relative efficiency,
Mean matrix,
Trace.

##### 1748 Geometrically Non-Linear Free Vibration Analysis of Functionally Graded Rectangular Plates

**Authors:**
Boukhzer Abdenbi,
El Bikri Khalid,
Benamar Rhali

**Abstract:**

In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.

**Keywords:**
Non-linear vibration,
functionally graded materials,
rectangular plates.

##### 1747 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.

##### 1746 A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides

**Authors:**
R. B. Ogunrinde,
C. C. Jibunoh

**Abstract:**

**Keywords:**
Spectral decomposition,
eigenvalues of the Jacobian,
linear RHS,
homogeneous linear systems.

##### 1745 Development of Admire Longitudinal Quasi-Linear Model by using State Transformation Approach

**Authors:**
Jianqiao. Yu,
Jianbo. Wang,
Xinzhen. He

**Abstract:**

This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

**Keywords:**
quasi-linear model,
simulation,
state transformation approach,
the ADMIRE model.

##### 1744 Asymptotic Stability of Input-saturated System with Linear-growth-bound Disturbances via Variable Structure Control: An LMI Approach

**Authors:**
Yun Jong Choi,
Nam Woong,
PooGyeon Park

**Abstract:**

Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.

**Keywords:**
Input saturation,
linear-growth bounded disturbances,
linear matrix inequality (LMI),
variable structure control

##### 1743 Variogram Fitting Based on the Wilcoxon Norm

**Authors:**
Hazem Al-Mofleh,
John Daniels,
Joseph McKean

**Abstract:**

**Keywords:**
Non-Linear Wilcoxon,
robust estimation,
Variogram
estimation.

##### 1742 Relationship between Sums of Squares in Linear Regression and Semi-parametric Regression

**Authors:**
Dursun Aydın,
Bilgin Senel

**Abstract:**

**Keywords:**
Semi-parametric regression,
Penalized LeastSquares,
Residuals,
Deviance,
Smoothing Spline.

##### 1741 Algorithms for the Fast Computation of PWL and PHL Transforms

**Authors:**
Fituri H Belgassem,
Abdulbasit Nigrat,
Seddeeq Ghrari

**Abstract:**

In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

**Keywords:**
Piece wise linear transforms,
Fast transforms,
Fast algorithms.

##### 1740 A Model-following Adaptive Controller for Linear/Nonlinear Plantsusing Radial Basis Function Neural Networks

**Authors:**
Yuichi Masukake,
Yoshihisa Ishida

**Abstract:**

**Keywords:**
Linear/nonlinear plants,
neural networks,
radial basisfunction networks.

##### 1739 Use of Linear Programming for Optimal Production in a Production Line in Saudi Food Co.

**Authors:**
Qasim M. Kriri

**Abstract:**

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

**Keywords:**
Parameter linear programming,
objective function,
sensitivity analysis,
optimize profit.

##### 1738 Recognition and Reconstruction of Partially Occluded Objects

**Authors:**
Michela Lecca,
Stefano Messelodi

**Abstract:**

A new automatic system for the recognition and re¬construction of resealed and/or rotated partially occluded objects is presented. The objects to be recognized are described by 2D views and each view is occluded by several half-planes. The whole object views and their visible parts (linear cuts) are then stored in a database. To establish if a region R of an input image represents an object possibly occluded, the system generates a set of linear cuts of R and compare them with the elements in the database. Each linear cut of R is associated to the most similar database linear cut. R is recognized as an instance of the object 0 if the majority of the linear cuts of R are associated to a linear cut of views of 0. In the case of recognition, the system reconstructs the occluded part of R and determines the scale factor and the orientation in the image plane of the recognized object view. The system has been tested on two different datasets of objects, showing good performance both in terms of recognition and reconstruction accuracy.

**Keywords:**
Occluded Object Recognition,
Shape Reconstruction,
Automatic Self-Adaptive Systems,
Linear Cut.

##### 1737 Parallel Alternating Two-stage Methods for Solving Linear System

**Authors:**
Guangbin Wang,
Ning Zhang,
Fuping Tan

**Abstract:**

In this paper, we present parallel alternating two-stage methods for solving linear system Ax = b, where A is a monotone matrix or an H-matrix. And we give some convergence results of these methods for nonsingular linear system.

**Keywords:**
Parallel,
alternating two-stage,
convergence,
linear system.

##### 1736 Determination of Geometric Dimensions of a Double Sided Linear Switched Reluctance Motor

**Authors:**
Dursun M.,
Koc F.,
Ozbay H.

**Abstract:**

**Keywords:**
Linear switched reluctance motor,
sliding door,
elevator door,
linear motor design.