梯形公式

对于记忆项的数值积分，采用了梯形公式与矩形公式结合的方法，并估计了数值积分的影响。

The trapezoidal rule is adopted for the quadrature of the memory term and the quadrature error is estimated .

本文介绍一种基于微分方程隐式积分梯形公式的电力系统稳定计算隐式积分交替求解算法。

This paper describes an implicit integration alternating solution method for power system dynamic stability simulation . The method is based on the trapezoidal rule of implicit integration in solving differential equations , which is numerically stable .

一种基于梯形公式的ODE算法2n阶非线性脉冲微分方程解的振动性

ODE Method for Solving Nonlinear Equation Oscillations of 2n Order Nonlinear ODE with Impulses

运用复合梯形公式作为求二重积分数值解的基本算法，采用Matlab软件编写程序，求解二重积分方程组。

Demand the use of double integral composite trapezoidal formula as the basic numerical solution algorithm , using Matlab software , programming , solve the double integral equations .

利用Green函数来求特解形式，把原来的二阶微分方程简化成一次积分形式，再由复化梯形公式求积法进行数值求解。

First we apply Green 's functions in special solution , simplifying the second order problems to the first order integral formulation , then we deal with its numerical solution by the compound trapezoidal formula .

推导出了复合梯形公式的一类渐近展开式，从另一方面印证了Euler-Maclaurin公式。

A asymptotic series of composite trapezoidal formula is obtained here , and Euler-Maclaurin formula is verified .

本文利用Euler-Maclaurin求和公式构造了一类求积公式，称为修正复合梯形公式。

In this aper , a kind of quadrature formulas are constructed by using the Euler Maclaurin summation formula .

基于梯形公式的柔体仿真算法的研究

Research on Flexible Object Simulation Algorithm Based on Trapezium Formula

梯形公式的推广和改进

The Extension and Improve of Trapezoid formula

复化梯形公式及其应用

Compound trapezoid formula and its application

一个修正复化梯形公式

A modified compound trapezoidal rull

采用最佳一致逼近多项式的方法，对传统梯形公式做了改进，从而进一步提高了数值积分抛物插值预处理法的精确度。

With the best polynomial approximation as a metric , we estimate the rate of Lp approximation and characterize the approximation order .

本文结果表明，当初值误差为零时，用形式简单的梯形公式即可满意地计算各种算法的总体误差。

The results show that , for many algorithm widely used in practice , the global error can be calculated satisfactory when the initial error equals to zero .

本文用梯形公式和辛普森公式给出了实际应用中可靠度计算的数值积分法，并与解析法做了比较。

A method of reliable calculation in the numerical value of integral is shown up in this article by using trapezoid formula and simpson formula in practical usage .

利用微分中值定理“中值点”的渐近性，给出一个新的积分梯形公式，由此得到定积分的估计式。

This paper intends to give a new integral trapezoid formula by using the asymptotic feature of mean value theorem of differential to conclude the estimated formula of definite integral .

采用梯形公式的四元组形式表达网络中的隶属函数，利用反向传播算法训练网络，得到较好的训练效率和效果。

This paper expresses membership function in the network by trapezium trapezoid formula . The network is trained using the improved back propagation algorithm , which can get better efficiency and effect .

将数值积分中的中矩形公式与梯形公式推广到两个函数的情形，并讨论了中间值的渐近性质。

The mid-rectangle formula and trapezoid formula are generalized , and as one of its application , a generalization of midpoint formula in numerical differentiation is obtained . The asymptotic property of obtained middle value is discussed .

本文提出了一种动态故障树顶事件发生概率的近似算法，该算法不需要把动态故障树转化为马尔可夫链，而是直接分析故障树模块，并用梯形公式得到近似数值解。

This paper introduces an approximate algorithm for top-event occurrence rate of dynamic fault trees . The method need not convert dynamic fault trees to Markov chains , but analyzes dynamic modules directly , and obtain approximate numerical solution using trapezoid formula .

借助于能量方程，提出了用梯形公式求解能量增量的方法，并就能量的分配进行了分析，建设采用耗能指标来衡量结构的破坏程度。

By means of energy equation , the authors put forward a ladder-shaped method to obtain the incremental forms of energy , and analyze the energy distributions , suggest that the parameter of energy dissipation be taken as the criterion of the structural damage .

提出用梯形积分公式和抛物线型积分公式代替FFT中的矩形积分公式，以提高FFT精度。

In order to improve the precision of FFT , the scheme of trapezoid and Simpson 's rule are substituted for normal rectangular integration in FFT .

关于在平行断面法资源/储量估算中限制使用梯形体公式的建议

Suggestions on Limiting the Use of Trapezoid Body Formula in Estimating Resource / Reserve by Using the Parallel Cross-section Method

经比较，可将此源于梯形积分公式的数值积分算法作为一种求解固体推进剂粘弹性参数的通用数值积分法。

This integration method that was originated from trapezoidal integration could be considered as a universal numerical integration method for solving the viscoelastic parameters of solid propellant .

利用复合Simpson数值积分方法、梯形面积型心公式和最优化理论对数学模型进行了精确求解，为平板车转弯工况的校核提供数值和理论依据，实现了平板车设计过程的实时、动态查询。

This paper uses Complex Simpson numerical integration , trapezium area formula and optimization theory to precisely compute according . to mathematical model . It provides data and reference to help check turning conditions of platform lorry , and realizes real time , dynamic inquiry of platform lorry design .

该文在深入分析阻尼梯形法误差的基础上，利用频谱观点，提出了修正的阻尼梯形法计算公式，使其稳态误差趋近于零。

Based on the deeply analysis of errors of Trapezoidal Integration with Damping , this paper presents its corrected calculating formula with the opinion of spectrum-analysis . The steady error of corrected arithmetic can converge to zero .