• Structural Engineering and Mechanics
• /
• 제20권6호
• /
• pp.713-726
• /
• 2005

Based on the improved first order Taylor interval expansion, a new interval analysis method for the static or dynamic response of the structures with interval parameters is presented. In the improved first order Taylor interval expansion, the first order derivative terms of the function are also considered to be intervals. Combining the improved first order Taylor series expansion and the interval extension of function, the new interval analysis method is derived. The present method is implemented for a continuous beam and a frame structure. The numerical results show that the method is more accurate than the one based on the conventional first order Taylor expansion.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제6권2호
• /
• pp.43-52
• /
• 2002

By the use of Taylor's expansion formula with the integral remainder, an accurate approximation for the fiber refractive index profile is given.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제22권2호
• /
• pp.125-136
• /
• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.

• 한국정밀공학회지
• /
• 제33권9호
• /
• pp.745-751
• /
• 2016

This paper presents the acceleration and deceleration control of free-form surfaces. A rapid variation of acceleration (or Deceleration) drives the system into a machine shock, resulting in the inaccuracy of the path control of the NURBS curve. The pattern of acceleration control can be established using the curvature of the NURBS curve. The curvature can be easily calculated from the first and second derivative of the NURBS curve used in Taylor's expansion for NURBS interpolation. However, the derivatives are not used in the recursive method for NURBS interpolation. Hence, we attempted the difference-derivatives for calculating the NURBS curvature. Both, Taylor's expansion and the recursive method, are used jointly for controlling the acceleration in the same interpolation algorithm.

• 한국정밀공학회지
• /
• 제12권6호
• /
• pp.145-151
• /
• 1995

The first-order Taylor series expansion can be evaluated analytically from the formulated symbolic nonlinear dynamic equations. A closed-form linear dynamic euation is derived about a nominal trajectory. The state space representation of the linearized dynamics can be derived easily from the closed-form linear dynamic equations. But manual symbolic expansion of dynamic equations and linearization is tedious, time-consuming and error-prone. So it is desirable to manipulate the procedures using a computer. In this paper, the analytic linearization is performed using the symbolic language MATHEMATICA. Two examples are given to illustrate the approach anbd to compare nonlinear model with linear model.

• 제어로봇시스템학회논문지
• /
• 제11권1호
• /
• pp.1-8
• /
• 2005

A new discretization algorithm for nonlinear systems with delayed input is proposed. The algorithm is represented by Taylor series expansion and ZOH assumption. This method is applied to the sampled-data representation of a nonlinear system with the time-delay input. Additionally, the delay in input is time varying and its amplitude is bounded. The maximum time-delay in input is assumed to be two sampling periods. The mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. The computer simulation proves the proposed algorithm discretizes the nonlinear system with the variable time-delay input accurately.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2005년도 ICCAS
• /
• pp.2562-2567
• /
• 2005

This paper suggests a new method discretization of nonlinear system using Taylor series expansion and zero-order hold assumption. This method is applied into the sampled-data representation of a nonlinear system with input time delay. Additionally, the delayed input is time varying and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. Them mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. And 'hybrid' discretization scheme that result from a combination of the ‘scaling and squaring' technique with the Taylor method are also proposed, especially under condition of very low sampling rates. The computer simulation proves the proposed algorithm discretized the nonlinear system with the variable time-delayed input accurately.

• Journal of applied mathematics & informatics
• /
• 제32권5_6호
• /
• pp.747-760
• /
• 2014

In this paper a higher order iterative algorithm is developed for an unconstrained multivariate optimization problem. Taylor expansion of matrix valued function is used to prove the cubic order convergence of the proposed algorithm. The methodology is supported with numerical and graphical illustration.

• Communications for Statistical Applications and Methods
• /
• 제21권3호
• /
• pp.253-260
• /
• 2014

The intraclass correlation model has a long history of applications in several fields of research. Case deletion diagnostic methods for the intraclass correlation model are proposed. Based on the likelihood equations, we derive a formula for a case deletion diagnostic method which enables us to investigate the influence of observations on the maximum likelihood estimates of the model parameters. Using the Taylor series expansion we develop an approximation to the likelihood distance. Numerical examples are provided for illustration.

• 대한수학회논문집
• /
• 제29권2호
• /
• pp.269-283
• /
• 2014

The aim of the paper is to present several new relationships involving the hyperharmonic function introduced by Mez$\ddot{o}$ in (I. Mez$\ddot{o}$, Analytic extension of hyperharmonic numbers, Online J. Anal. Comb. 4, 2009) which is an analytic extension of the hyperharmonic numbers. These relations are obtained by using some fractional calculus theorems as Leibniz rules and Taylor like series expansions.