A multilevel univariate cubic spline quasi-interpolation and application to numerical integration

Li, Caiyun; Zhu, Chun‐Gang

doi:10.1002/mma.1272

Cited by 7 publications

(3 citation statements)

References 11 publications

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“…A smooth curve is constructed using ordered value points so that the curve passes sequentially through the sampling points. There are many methods for curve interpolation, such as polynomial curve interpolation, cubic Hermit interpolation, cubic parametric spline interpolation, multinode spline interpolation, algebraic interpolation, circular spline interpolation, and quasi-interpolation [16][17][18]. The adaptive cubic B-spline curve interpolation based on error control can adjust the number of interpolation points according to a preset error [19].…”

Section: Curve Fitting and Interpolation Of Discrete Velocity Pointsmentioning

confidence: 99%

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Engine power measurement without external load based on vibration signal

Zhang¹,

Zeng²

2017

J. vibroeng.

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The vibration signals from engines contain information about the engine conditions. Engine power is an important parameter that indicates the state of an engine. In this manuscript, a method for measuring the engine power, using the vibration signals from the engine, is developed. In our proposed method, the power of the engine is measured based on the principle of no-load measurement. The discrete values of rotation speed are computed from the vibration signal, using wavelet transforms, the Hilbert envelope, and three autocorrelations. By comparing various curve-fitting and interpolation methods, an optimal method for curve fitting the discrete acceleration data is chosen, and the corresponding times of the starting speed and terminal speed are calculated using the analytical formulas of the fitted curve. Finally, the maximum engine power is obtained from the calibration tests. Experimental results show that the overall performance is good and that the maximum power measurement accuracy is 98.4 % after accurate calibration. This meets the requirements of the power measurement accuracy under the condition of no load.

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Section: Curve Fitting and Interpolation Of Discrete Velocity Pointsmentioning

confidence: 99%

“…By means of steady-state tests using a dynamometer, we obtained the moment of inertia of the engine and then calculated the average power using Eq. (18). We had calculated the average power, but it will change with the selected starting and terminal speed changes.…”

Section: Optimal Fitting Scheme Selection and Power Acquisition Basedmentioning

confidence: 99%

Engine power measurement without external load based on vibration signal

Zhang¹,

Zeng²

2017

J. vibroeng.

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“…Traveling wave solutions of generalized forms of Burgers and Burgers-KdV were obtained with the standard tanh method. 3,19 Li and Zhu 20 proposed a multilevel univariate quasi-interpolation scheme which was applied to numerical integration. Bhatti et al 21,22 discussed the effects of heat transfer and Hall current on the sinusoidal motion of solid particles through a planar channel.…”

Section: Introductionmentioning

confidence: 99%

Cubic B-spline quasi-interpolation and an application to numerical solution of generalized Burgers-Huxley equation

Sun

Zhu

2020

Advances in Mechanical Engineering

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Nonlinear partial differential equations are widely studied in Applied Mathematics and Physics. The generalized Burgers-Huxley equations play important roles in different nonlinear physics mechanisms. In this paper, we develop a kind of cubic B-spline quasi-interpolation which is used to solve Burgers-Huxley equations. Firstly, the cubic B-spline quasi-interpolation is presented. Next we get the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and modified Euler scheme to approximate the time derivative of the dependent variable. Moreover, the efficiency of the proposed method is illustrated by the agreement between the numerical solution and the analytical solution which indicate the numerical scheme is quite acceptable.

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