Papers by Keyword: Chebyshev Polynomial

Abstract: Modern automobile design technology often employed finite element analysis and computational fluid dynamics, which are computational expense and highly time cost and need to employ approximation techniques. We herein study a Chebyshev Polynomial Model-based approximation technique, and employ it for predictive design. Firstly, we investigated the multi-valuable function prediction on the model precision. We also employed cross-validation as error analysis method. The computational results from expensive optimization of CEC 2014 tested our predictive methods. The experimental results showed that the proposed method is suitable for solving the low dimensional function prediction problems.

Abstract: In this paper, we study the chaos control in the fractional-order Lorenz system with random parameter. Firstly, according to orthogonal polynomial approximation principle of the Functional analysis, the fractional-order Lorenz system with random parameter is reduced to its equivalent deterministic one. Secondly, chaos control equivalent deterministic system research using the linear feedback method. Finally, though numerical results show the effective and feasible of this method.

Abstract: The paper is devoted to the numerical stability of fractional delay differential equations with non-smooth coefficients using the Chebyshev collocation method. In this paper, based on the Grunwald-Letnikov fractional derivatives, we discuss the approximation of fractional differentiation by the Chebyshev polynomial of the first kind. Then we solve the stability of the fractional delay differential equations. Finally, the stability of the delayed Mathieu equation of fractional order is examined for a set of case studies that contain the complexities of periodic coefficients, delays and discontinuities.

Abstract: Many factors may affect array induction log, including skin effect. In this paper, according to relative formula deduced, a correction method of skin effect based on multi-frequency measurement signals is proposed using only the real component. This paper gives apparent conductivities that are from first order derivative correction and second order derivative correction by Chebyshev polynomial fitting method. Compared with measured data calculation, it showed that the correction results from the method above were in good agreement with the data from Express software.