常微分方程是大自然的语言。
The Ordinary differential equation is the language of the nature.
该常微分方程可用扩展的F展开法求解。
常微分方程中经典的存在性定理不能使用。
Often the existence axioms of classic in the differential calculus square distance can't use.
非常好的东东，可以用来求解常微分方程。
Dongdong very good and can be used to solve ordinary differential equations.
他的工作在数学上就停留在常微分方程的范围。
His work remains mathematically in the realm of ordinary differential equations.
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.
常微分方程的边值问题是微分方程的一个重要研究领域。
The boundary value problem of ordinary differential equations is an important domain in differential equations.
提出求解常微分方程的一种新的数值方法——解析离散法。
A new numerical method, analytical discrete method, for solving ordinary differential equations is proposed.
本文研究了二阶变系数线性常微分方程的一种近似求解方法。
In this paper, we study an approximate solution of the second-order linear ordinary differential equations with variable coefficients.
利用这一公式建立了常微分方程初值问题的正交多项式拟合算法。
By using this formula, orthogonal polynomial fitting algorithm for initial value problems of ordinary differential equations is established.
结果表明，该方法对于求解各类变系数常微分方程是十分有效的。
The result shows that it is effective for solving ordinary differential equation with variable coefficients.
利用常微分方程的不变式，非常方便地求解了一些量子力学问题。
Some problems of quantum mechanics can be solved easily by means of the invariant of differential equation.
对峙反应动力学过程，其实质是一个求解一阶常微分方程的过程。
Essentially, the opposite reaction kinetics process is a process of resolving the first order ordinary differential equation.
本文用四维相空间和四阶自洽常微分方程描写了单摆的受迫振动。
The forced vibration of pendulum is described by four-dimensional phase space and the fourth order autonomous ordinary differential equation.
常微分方程边值问题是常微分方程理论研究中最为重要的课题之一。
The ordinary differential equation singular boundary value problem is one of the most important branches of ordinary differential equations.
常系数的常微分方程变换为代数方程可以用于实现传递函数的概念。
Ordinary differential equation with constant coefficients transform into algebraic equations that can be used to implement the transfer function concept.
在建立单元的能量方程后，对方程进行变分得到墙元的常微分方程。
When energy equation for element was built, variational method was used to get ordinary differential equation.
在常微分方程论中，微分不等式是研究方程解的各种属性的有用工具。
Among ordinary differential equation equations, differential inequality is a useful tool which helps research on properties of equation-solving.
文摘：利用常微分方程的不变式，非常方便地求解了一些量子力学问题。
Abstract: Some problems of quantum mechanics can be solved easily by means of the invariant of differential equation.
本文对几类二阶非线性常微分方程，利用首次积分求得了其通积分公式。
This paper has found general integral formulas of some types of two - order nonlinear ordinary differential equations by first integral.
在这种方法中，我们可以在对常微分方程进行积分的过程中自由选择步长。
In this approach we have the freedom in the choice of step size during the integration of the ordinary differential equation.
文中得到几个振动性准则和离散谱准则，并将这些结果应用到常微分方程。
Some oscillatory criteria and discrete spectrum criteria are given, and we can apply them to the ordinary differential equations.
利用常微分方程定性理论的方法讨论了价格成本变化的单种群经济捕获模型。
Using method of qualitative theory of ordinary differential equation, studies economic harvesting model with variable price and cost for a single population.
用求解常微分方程及其初值问题的方法得到由函数方程表示的基本初等函数。
The basic elementary functions represented by functional equations were obtained by using the methods of solving ordinary differential equations and initial value probe.
许多环境数学模型是用常微分方程表示的，它只考虑了时间对种群密度的影响。
Many environment mathematical models are ordinary differential equations where time is considered only as its effect on population density.
讨论了解常微分方程的积分因子法在极限理论、微分学、积分学中的一些应用。
Some simple application of method of integrating factor that solve ordinary differential equation is discussed on the limit theory, differential and integral.
为了更合理的描述汇流过程，建模时应用随机微分方程替代确定性常微分方程。
The stochastic differential equation is used to replace the ordinary differential equation to describe the process of the flow concentration more reasonable.
基于常微分方程数学模型建立了多体系统动力学设计灵敏度分析的伴随变量方法。
The adjoint variable method for design sensitivity analysis of multibody system dynamics based on ordinary differential equations is presented.
基于常微分方程数学模型建立了多体系统动力学设计灵敏度分析的伴随变量方法。
The adjoint variable method for design sensitivity analysis of multibody system dynamics based on ordinary differential equations is presented.
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