共查询到20条相似文献,搜索用时 93 毫秒
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利用带有积分余项的Taylor公式重新推导了Simpson校正公式,同时给出了其误差的精确表示,而这一结果将优于Simpson校正公式[J]中的误差估计. 相似文献
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通过一阶导数对Simpson不等式进行了改进,并推导出了相应的数值积分公式和最佳误差限,扩大了Simpson积分公式的适用范围,最后给出了具体的数值应用. 相似文献
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通过对Ostrowski不等式的改进,扩大了Ostrowski积分公式的适用范围,将该积分公式应用于数值积分推广了经典的中点积分公式、梯形积分公式和Simpson积分公式,同时得到相应的最佳误差限,并给出了具体的数值应用. 相似文献
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提出了一类计算定积分的高精度柯特斯校正公式,通过两种方法进行了推导,给出了它的复化公式及其加速公式,并得到了它们的误差估计和收敛阶.数值实验验证了复化柯特斯校正公式及其加速公式的高效性. 相似文献
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数值积分公式中间点的渐近性质及其应用 总被引:17,自引:1,他引:16
主要研究了三类数值积分公式的中间点的渐近性质,得到了更一般性的结果.基于中间点的渐近性质,获得了数值积分的校正公式及其条件误差估计.数值例子显示了校正公式的精度明显高于对应的计算公式. 相似文献
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《数学的实践与认识》2015,(5)
采用有限元法分析柔顺机构的动力学性能时需要建立相应的柔性铰链的单元刚度矩阵和单元质量矩阵.先建立了双轴柔性铰链的数学模型,用数学归纳法推导了高阶余弦函数降阶为一次余弦函数的表达式,并求解了双轴柔性铰链单元质量矩阵的闭式解析式.比较了闭式解析式与其它数值积分如复化梯形公式、复化Simpson公式、Gauss-Legendre公式、Gauss-Chebyshev公式、Romberg积分等的积分精确度,表明采用本方法是非常适用且精确度是最高的. 相似文献
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Jesse Y. Wang 《BIT Numerical Mathematics》1976,16(2):205-214
A method of estimating the discretisation error for the weighted Simpson rule is given. The results are used to obtain the convergence rates of a numerical method for solving integral equations with various singular kernel functions. 相似文献
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The main objective of this work is to give a necessary and sufficient condition for the function defined as the difference of the Simpson quadrature rule and the arithmetic integral mean to be Schur-convex. 相似文献
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We propose a new variant of Newton’s method based on Simpson’s three-eighth rule. It can be shown that the new method is cubically convergent. 相似文献
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Nenad Ujević 《Journal of Applied Mathematics and Computing》2007,24(1-2):65-79
An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson’s rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given. 相似文献
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Summary. Using a method based on quadratic nodal spline interpolation, we define a quadrature rule with respect to arbitrary nodes,
and which in the case of uniformly spaced nodes corresponds to the Gregory rule of order two, i.e. the Lacroix rule, which
is an important example of a trapezoidal rule with endpoint corrections. The resulting weights are explicitly calculated,
and Peano kernel techniques are then employed to establish error bounds in which the associated error constants are shown
to grow at most linearly with respect to the mesh ratio parameter. Specializing these error estimates to the case of uniform
nodes, we deduce non-optimal order error constants for the Lacroix rule, which are significantly smaller than those calculated
by cruder methods in previous work, and which are shown here to compare favourably with the corresponding error constants
for the Simpson rule.
Received July 27, 1998/ Revised version received February 22, 1999 / Published online January 27, 2000 相似文献
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Fourier analysis plays a vital role in the analysis of continuous‐time signals. In many cases, we are forced to approximate the Fourier coefficients based on a sampling of the time signal. Hence, the need for a discrete transformation into the frequency domain giving rise to the classical discrete Fourier transform. In this paper, we present a transformation that arises naturally if one approximates the Fourier coefficients of a continuous‐time signal numerically using the Simpson quadrature rule. This results in a decomposition of the discrete signal into two sequences of equal length. We show that the periodic discrete time signal can be reconstructed completely from its discrete spectrum using an inverse transform. We also present many properties satisfied by this transform. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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P. Bocher H. De Meyer G. Vanden Berghe 《Journal of Computational and Applied Mathematics》1994,50(1-3):145-158
Gregory-type formulae associated with the class of composite Newton—Cotes quadrature rules of the closed type are established. Furthermore, it is shown how these formulae can be extended by introducing mixed interpolation functions which contain a polynomial and a trigonometric part. The case of the modified Gregory rules associated with the composite Simpson quadrature rule is worked out in detail. Also the error term is analysed and the obtained rules are numerically tested. 相似文献
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In this paper, an approximate method for the numerical integration of singularly perturbed two-point boundary-value problems with a boundary layer on the left end of the underlying interval is presented. The method is distinguished by the following fact: the original second-order differential equation is replaced by an approximate first-order differential equation with a small deviating argument and is solved efficiently by employing the Simpson rule, coupled with the discrete invariant imbedding algorithm. The proposed method is iterative on the deviating argument. Several numerical examples have been solved to demonstrate the applicability of the method. 相似文献