共查询到19条相似文献,搜索用时 171 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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基于直接数值积分的Laplace逆变换方法的比较研究 总被引:5,自引:0,他引:5
为了探讨各种数值积分方法,如梯形公式、Simpson法、Gauss积分方法和振荡函数积分方法等,在数值Laplace逆变换中的应用效果,本文进行了基于各种离散数值积分公式的Laplace逆变换方法的比较研究,涉及到24种方法,针对Davies和Martin的16个考题,给出了数值比较结果,得出了一些新的结论。 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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本文对Stiff常微分方程组初值问题,应用梯形公式外插所得到的值以及它同Simpson公式所得到的值进行适当的线性组合而得到两个Stiff稳定的单步四阶“块”数值方法簇,此外,在得到数值解的同时,还得到局部截断误差的具体值。最后给出了数值实验。 相似文献
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将不等距离分割方法与人工鱼群算法相结合,提出一种基于人工鱼群算法求任意函数数值积分的方法,该方法除能计算通常意义下任意函数的定积分外,还能计算奇异函数积分、振荡函数积分以及原函数不易求得的被积函数的积分.最后给出几个数值积分算例,并与传统数值积分方法作了比较,仿真结果分析表明,该算法十分有效,能够快速有效地获得任意函数的数值积分值. 相似文献
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Shaoqin ZHANG 《Frontiers of Mathematics in China》2016,11(2):461-496
Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established. 相似文献
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Huriye
Kadakal 《Numerical Methods for Partial Differential Equations》2020,36(6):1555-1565
In this study, using power-mean inequality and improved power-mean integral inequality better approach than power-mean inequality and an identity for differentiable functions, we get inequalities for functions whose derivatives in absolute value at certain power are convex. Numerically, it is shown that improved power-mean integral inequality gives better approach than power-mean inequality. Some applications to special means of real numbers and some error estimates for the midpoint formula are also given. 相似文献
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Kuang JichangLokenath Debnath 《Journal of Mathematical Analysis and Applications》2002,267(1):395-399
An extension of Carlson's inequality is made by using the Euler-Maclaurin summation formula. The integral analogues of this inequality are also presented. 相似文献
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一个第二类变分不等式的有限元逼近 总被引:1,自引:0,他引:1
本短文讨论下述第二类变分不等式(见 [2, 4])的有限元逼近及其误差分析:其中是平面凸多边形区域的的边界, 且而 . 诸如热量控制问题,流体通过半可透性壁的扩散问题以及简化库仑摩擦接触问题的正则化方法等均可归为上述变分不等式(1)(见[2,3]).在文[2]中给出了上述变分不等式的有限元逼近格式,作出了收敛性分析及误差估计.本文的目的是进一步用数值积分简化上述有限元逼近格式并改进原有的估计误差. 设Th是的拟一致三角形部分,Vh是对应的线性元空间,且使得vh=0在上.[2]中用数值积分代替其中 Mi… 相似文献
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An interesting property of the midpoint rule and the trapezoidal rule, which is expressed by the so-called Hermite-Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite-Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. In particular, for simplices of arbitrary dimension, we present two families of integration formulae which both contain a multivariate analogue of the midpoint rule and the trapezoidal rule as boundary cases. The first family also includes a multivariate analogue of a Maclaurin formula and of the two-point Gaussian quadrature formula; the second family includes a multivariate analogue of a formula by P.C. Hammer and of Simpson's rule. In both families, we trace out those formulae which satisfy a Hermite-Hadamard inequality. As an immediate consequence of the latter, we obtain sharp error estimates for twice continuously differentiable functions.
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关于内积空间中逆Cauchy-Schwarz不等式的一些结果 总被引:1,自引:0,他引:1
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz‘s inequality is provided. The results obtained in the paper complement and improve some recent work about this topic. 相似文献
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关于含有Wallis公式的双边不等式 总被引:8,自引:2,他引:6
赵德钧 《数学的实践与认识》2004,34(7):166-168
得到了含有 Wallis公式的一个简洁且更为精细的双边不等式 . 相似文献
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In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality. 相似文献