将精细积分法用于求解波动方程。
A precise integration method was applied to solve wave equation.
最后利用经典的精细积分方法求解该方程组。
At last, those differential equations are solved by the classic precision integration method.
精细积分法是求解常微分方程的一种成熟的数值算法。
Time precision integration method is a mature numerical algorithm to solve the ordinary differential equation.
一维扩散方程初值问题可以用全域或子域精细积分求解。
The initial problem of one dimensional diffusion equations can be solved by using global or sub domain high precise integration method.
可用单内点子域精细积分，求解对流-扩散方程初值问题。
Initial value as a problem of convection diffusion equation can be solved by applying fine integral of single inner point subdomains.
可用单内点子域精细积分法，求解二维抛物型方程初值问题。
The initial-value problem of two-dimensional parabolic equation can be solved by using meticulous integration of single inner point subdomain.
在瞬态温度场正问题求解中采用了精细积分方法以提高计算精度。
The precise integral method is used to solve the instantaneous heat transfer equations to improve solution precision.
将作者提出的高精度任意阶显式精细积分多步法应用于刚性方程中。
The arbitrary order explicit precise time integration method with high accuracy is developed to sti? Equations.
通过矩阵变换，利用矩阵对称性、子结构等方法改进精细积分计算效率。
Utilizing the symmetry of matrices and the idea of substructure, the computational precision and efficiency of the PIM are improved.
在原有精细积分法的基础上，对非齐次方程出现奇异矩阵的问题进行探讨。
Based on the original precise integration method, the problem that singular matrix appears in non-homogeneous equation was discussed.
周期时变线性系统系数矩阵的时变性与不可交换性是其精细积分算法设计中的瓶颈。
The time-varying and incommutable character of the coefficient matrix of periodically time-varying linear systems are the bottleneck of the design for high precision direct integration methods.
采用了模态变换和精细积分法，解决了考虑多阶模态的阻尼矩阵给求解所带来的困难。
To overcome the difficulties in the solving process brought by the multi-modal damping model, the modal transformation strategy and the precise time-integration method are applied.
对线性定常结构的动力系统提出的精细积分法，能得到在数值上逼近于精确解的结果。
The precise integration method proposed for linear-invariant dynamic system can give precise numerical results approaching to the exa ct solution at the integration points.
与更新精细积分法相比，在实现动力微分方程降阶后，矩阵尺度和方程个数减少一半；
When the order of dynamic differential equation is reduced, the size of matrices and equations of the proposed method are only half of that of the RPTSIM.
提出精细积分半解析法求解变系数的以超孔压和孔隙比为控制变量的渗压固结微分方程。
A precise time step integration method was proposed to solve the finite strain osmotic consolidation equation with varied coefficients.
数值算例表明，用精细积分法得到的解与精确解十分吻合，比有限差分法具有更高的精度。
The results of the precise integration method agree well with the theoretical solution and have higher precision than those of the finite difference method.
钟万勰院士提出的偏微分方程的子域精细积分方法是一种半解析方法，方法简单，精度高。
The Precise Integration Method in the time domain developed by Zhong is very useful to solve a kinds of differential equations because it possesses very high efficiency and accuracy.
在精细时程积分法的基础上，将精细积分法与振型叠加法结合起来，提出振型分解精细积分法。
This new method is called the mode decomposition precise integration method because it is the result of the combination of the mode decomposition method with the precise integration method.
基于齐次扩容精细积分法，提出了求解复杂载荷作用下任意外形弹性拱平面弯曲的一种新方法。
Based on the extended homogeneous capacity precision integration method, a novel method was presented for solving plane bending problems of elastic arches with arbitrary profile.
首先将非线性薛定谔方程变形为齐次方程的形式，然后用精细积分法模拟其随时间的演化过程。
First of all, a non-linear Schrodinger equation can be converted into homogeneous equations, and then the precise integration method can be used to solve these problems.
在动力分析方法方面，本文将精细积分法应用到短肢剪力墙结构中，提出了纽马克—精细时程法。
Precise time integration method is applied in short-leg shear wall, and a new scheme is put forward which is referred as Newmark-precision time history method.
数值算例结果表明该法能够明显提高计算效率，在显式积分区域和精细积分区域都有很高的精度。
Numerical examples demonstrate that the proposed method can obviously increase computation efficiency and has higher accuracy in both kinds of integration regions.
对于非线性动力学问题，给出了一个显式的精细积分算法，适用于多自由度、强非线性、非保守系统。
An explicit precise integration for nonlinear dynamics problems is presented, which is suitable to solve the non-conservative systems with multi-DOF and strong nonlinearity.
利用精细积分技术对同伦摄动方法进行了改进，构造了一种求解非线性动力学方程的新的渐近数值方法。
A new asymptotic numerical method for nonlinear dynamic equations was proposed. In this method, the homotopy perturbation method was improved by using the precise integration technique.
本文将钟万勰院士提出的精细积分法应用到载荷识别中去，得到了在不同输入输出条件下的载荷识别公式。
Precise integration method is used in this paper to the problem of loading identification and loading identification formulas in variant input and out put conditions are gotten.
提出了一种求解一类非齐次线性常微分方程的精细积分方法，通过该方法可以得到逼近计算机精度的结果。
Precise integration method for a kind of non-homogeneous linear ordinary differential equations is presented. This method can give precise numerical results approaching the exact solution.
文末的数值算例进一步表明，精细积分法对大的时间步长和长时间计算均有效，因此是一种很实用的方法。
Results show that this method has high accuracy even for very large time-step sizes, and possesses excellent long-time numerical calculation behavior.
该模型的建立为应用新型齐次扩容精细积分技术，构建一种高效率和高精度的半解析半数值方法奠定了基础。
The model lays a foundation for applying the technologies of homogenized precise integration and building a semi-analytical and semi-numerical method with high efficiency and accuracy.
将小波配置方法和精细积分方法相结合，提出了一种对水土侵蚀模型进行数值分析的新方法——小波精细积分法。
A new numerical method on rill erosion model was proposed by combining the wavelet collocation method with the precise integration method, which is called wavelet precise integration method (WPIM).
将小波配置方法和精细积分方法相结合，提出了一种对水土侵蚀模型进行数值分析的新方法——小波精细积分法。
A new numerical method on rill erosion model was proposed by combining the wavelet collocation method with the precise integration method, which is called wavelet precise integration method (WPIM).
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