[數] 常微分方程
The result shows that it is effective for solving ordinary differential equation with variable coefficients.
結果表明，該方法對于求解各類變系數常微分方程是十分有效的。
This paper proves that the quasilinearization method for parameter estimation of ordinary differential equation in chemical reaction kinetics essentially belongs to the region of Gauss-Newton method.
本文通過理論推導，證明在反應動力學常微分方程參數估值中所采用的拟線性化法在本質上仍然屬于高斯—牛頓法的範疇。
In this paper based upon the knowledge of ordinary differential equation and its stability theory, we study the solutions of Dirac equation.
本文主要利用常微分方程的基本理論及其定性理論，采用打靶法研究狄拉克方程解的存在性問題。
When energy equation for element was built, variational method was used to get ordinary differential equation.
在建立單元的能量方程後，對方程進行變分得到牆元的常微分方程。
A non-linear ordinary differential equation involving topographic forcing and zonal shear basic flow is derived using phase angle function with semi-geostropical approximation.
在半地轉近似下，用相角函數方法得到了含地形強迫作用與緯向切變基流的非線性常微分方程。
This paper discusses a class of biochemical reaction system with doubly saturated reaction speed by using the method of qualitative theory of ordinary differential equation.
利用常微分方程定性理論的方法，讨論了一類具有二重飽和反應速度的生化反應模型。
From then on plenty of work had been done to research the periodic solution and stability of ordinary differential equation.
此後大量的工作研究常微分方程的周期解、穩定性，這在一定程度上解釋了種群的共存、滅絕、持續生存。
This paper applies an ordinary differential equation (ODE) solver of interpolating matrix method to calculate large deflection of thin circular plate with varible thickness.
文章用插值矩陣法的常微分方程求解器求解變厚度圓薄闆大撓度彎曲問題，提出了對一般方程正則奇點的處理途徑。
The CAI teaching of a first-order ordinary differential equation is discussed with computer MATLAB software, and its feasibility and convenience is introduced.
利用MATLAB進行一階常微分方程的計算機輔助教學，探讨用MATLAB進行一階常微分方程輔助教學的可行性、方便性。
By the Kantorovich approximation method with generalized beam functions, an ordinary differential equation and the boundary conditions for plate vibrations are derived.
然後在王磊教授工作的基礎上再次采用康托洛維奇能量近似法結合廣義梁函數，導得闆振動的一個常微分方程及邊界條件。
This course consists of several major parts such as ordinary differential equation vectors and analytic geometry derivatives integration and series.
課程内容包括常微分方程、空間解析幾何與向量代數、多元函數微分學、多元函數積分學和無窮級數等幾大闆塊。
Solving process of monotonic iteration to the initial value question of non-continuous ordinary differential equation of the first order is discussed, the known results are generalized.
讨論一階非連續常微分方程初值問題的單調疊代求解，推廣了已知結果。
Among ordinary differential equation equations, differential inequality is a useful tool which helps research on properties of equation-solving.
在常微分方程論中，微分不等式是研究方程解的各種屬性的有用工具。
The ordinary differential equation of round laminar jet of power-law fluid is derived, and the solution of this equation by numerical integration is obtained.
用層流邊界層方程，導出幂律流體軸對稱層流自由射流的常微分方程，并給出其方程的數值解。
The conditions of three elementary static bifurcations as saddle-node, transcritical, and pitchfork types of bifurcations for a one-dimensional ordinary differential equation are formulated.
推導出一維非線性微分動力系統發生鞍結分岔、跨臨界分岔和叉形分岔三種基本平衡點分岔的條件。
The series solutions of the linear ordinary differential equation at singular point were stu***d via the infinite order matrix of the linear differential operator in power series basis.
應用線性微分算子在幂基下的無限階矩陣，研究線性微分方程在奇點處的級數解。
By using qualitative classical theory of ordinary differential equation, a class of planar quintic polynomial differential system is qualitatively analyzed.
采用常微分方程定性理論的經典方法，對一類平面五次多項式系統進行定性分析。
A second_order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained. And the first integral of the equation was then carried out.
得到了描述球殼内表面運動的二階非線性常微分方程，并給出了方程的首次積分。
Method of leading variables is method of solving linear ordinary differential equation of first order.
常數變易法是作為求解一階線性方程的解法給出的。
Using variable size array instead fixed array can save EMS memory and acceleration the calculate speed. COLSYS has been choosed to be a ordinary differential equation solver in the program.
程式選用COLSYS為常微分方程求解器，繼承并發展了前人的成果，因此程式同樣能計算穩态問題。
In this approach we have the ******* in the choice of step size during the integration of the ordinary differential equation.
在這種方法中，我們可以在對常微分方程進行積分的過程中自由選擇步長。
The buckling equation of pipe string in horizontal boreholes is a fourth non-linear ordinary differential equation with a small parameter.
管柱在水平井眼中的屈曲方程是一個含有小參數的四階非線性常微分方程。
Many of the exact solutions of (3+1) dimensional breaking soliton equation are obtained by using a ****** transformation relation and solving the ordinary differential equation.
首先通過變換關系和求解簡單的常微分方程，得到了（3+1）維破裂孤子方程豐富的孤立波解和周期波解。
An annular model for chemostat was depicted by a group of ODE(ordinary differential equation) to imitate the ecosystem which included competition and predator-prey relations in nature.
為模拟自然界中既包含競争關系又包含捕食-被捕食關系的生态系統，建立用常微分方程組表示的環狀模型。
Some ****** application of method of integrating factor that solve ordinary differential equation is discussed on the limit theory, differential and integral.
讨論了解常微分方程的積分因子法在極限理論、微分學、積分學中的一些應用。
|ordinary differentical equations/ODEs;[數]常微分方程
常微分方程（Ordinary Differential Equation, ODE） 是指隻包含一個自變量、一個或多個未知函數及其導數的方程。它用于描述物理、工程、生物、經濟等領域中系統狀态隨單一變量（通常是時間或空間）變化的動态規律。
方程中僅涉及一個獨立變量（如時間 $t$ 或位置 $x$），區别于偏微分方程（PDE）的多自變量特性。
方程包含未知函數（如 $y(t)$）及其一階或高階導數（如 $frac{dy}{dt}$, $frac{dy}{dt}$）。
根據方程類型選擇不同解法：
注：引用來源為學術教材及公開課程資源，鍊接因平台限制未展示，可通過來源名稱檢索原文。
常微分方程（Ordinary Differential Equation，ODE）是數學中研究單變量函數及其導數關系的方程，主要描述一個未知函數與其自變量之間的動态變化規律。
階數
由方程中最高階導數決定。例如：
線性與非線性
例如，方程 ( frac{dy}{dx} = ky ) 的通解為 ( y = Ce^{kx} )，描述指數增長或衰減過程。
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