1) second-order differential equation
二级微分方程
3) second order differential equations
二阶微分方程
1.
The problem on stability of second order differential equations with both impulse and delay is investigated.
研究了带脉冲和时滞的二阶微分方程的稳定性问题。
2.
Some oscillation criteria are given for certain second order differential equations by using an integral averaging technique.
利用积分平均技巧研究二阶微分方程(r(t)(x(t) )x′(t) )′+ q(t) f(x(t) ) g(x′(t) ) =0 。
3.
We study some twist second order differential equations.
本文研究了具有扭转性的二阶微分方程,证明在一定条件下通过角函数的扭转所表述的几何性质可以得到周期解的存在性。
4) second-order ordinary differential equation
二阶常微分方程
1.
Second-order ordinary differential equations arise in a wide variety of scientific and engi-neering applications, including celestial mechanics, theoretical physics and chemistry, electronicsand semi-discretisation of partial differential equation.
二阶常微分方程在天体力学、理论物理与化学、电子学以及偏微分方程的半离散等领域具有广泛的应用。
2.
This paper deals with numerical methods for the second-order ordinary differential equations y″(x)=f(x,y) and their numerical stability property.
主要研究二阶常微分方程初值问题y″(x)=f(x,y)的数值方法及其数值稳定性。
5) second order differential equation
二阶微分方程
1.
The existence of positive homoclinic orbits is obtained by the variational approach for a class of the second order differential equations-α(x)u+β(x)u2+γ(x)u3=0,where the coefficient functions α(x),β(x),γ(x) satisfy xα′(x)≥0,xβ′(x)≤0,xγ′(x)≤0 for all x∈R.
运用变分方法证明了一类二阶微分方程-α(x)u+β(x)u2+γ(x)u3=0,x∈R的正同宿轨存在性,其中系数函数α(x),β(x),γ(x)满足xα′(x)≥0,xβ′(x)≤0,xγ′(x)≤0对任意x∈R成立。
2.
Research on the solution s existence-uniqueness and singular perturbation for a class of boundary value problem of second order differential equation,using the results obtained,research the singular perturbation for boundary value problem of second order semi-linear differential equation.
研究一类二阶微分方程边值问题的微分不等式理论与解的存在唯一性,利用所得结论研究其二阶拟线性微分方程边值问题的奇异摄动现象。
3.
In this paper,we research the singular perturbation for boundary value problem of second order differential equation with two small parameter as following:{εy″= f(t,y,y′,ε,μ),a < t < by(a,ε,μ) = A(ε,μ),y(b,ε,μ)=B(ε,μ) under the condition of strong stability.
研究在强稳定条件下的具有两个小参数的二阶微分方程的边值问题{εy″=f(t,y,y′,ε,μ),a
6) differential equation of second order
二阶微分方程
1.
The energy eigenvalues of three-dimensional harmonic oscillator and hydrogen atom are solved by using supersymmetric WKB approximate method;the eigenvalue of angular momentum and angular dimension of non-central potential are gained by applying SWKB theory to differential equation of second order including angular coordinate.
运用超对称准经典近似方法给出三维谐振子、氢原子的能谱,进而将该方法用于含角坐标的二阶微分方程,得到角动量平方L2的本征值和非中心势的角向本征值。
2.
In this paper, we studied oscillatory properties of a differential equation of second order and used the differential inequality for coefficient of differential equation to judge oscillation of equation.
研究了一类二阶微分方程的振动性质,利用方程的系数满足的微分不等式来判断方程的振动性。
3.
With the results we studied oscillatory properties of differential equation of second order by using the results.
讨论了一般的 Euler方程解的振动性 ,并利用它研究了二阶微分方程的振动性
补充资料：微分方程的差分方程逼近
微分方程的差分方程逼近
approximation of a differential equation by difference equations
微分方程的差分方程通近【app拟。mati.ofa山价犯n-ti习闪姗柱.by山血魂.理equa西姗;即即肠。砚田朋.朋巾卜碑四.别吸.。印冲.旧e朋，pa3I.ecTll目M] 微分方程用关于未知函数在某种网格上的值的代数方程组的逼近，当网格的参数(网络、步长)趋于零时可使得逼近更加精确. 设L(Lu可)是某个微分算子，几(L声。=几，。。任叭，人“凡)是某个有限差分算子(见徽分算子的差分算子通近(aPProximation of a dilferential operator by dif-feren沈。perators”.如果算子L、关于解u逼近算子L，其阶为p，即如果 }}Lh[u]*I}汽=o(hp)，那么有限差分式L声、二0(o任凡)称为关于解“对微分方程Lu=O的P阶逼近. 构造有限差分方程L声*=0关于解u逼近微分方程Lu=0的最简单例子是将Lu的表达式中每个导数用相应的有限差分来代替. 例如，方程 _子“.，、血._，_八_一n Lu三书舟+P(x)于+q(x)u=U ~“一dxZr‘~产dxl‘’可用有限差分方程 L‘“‘三生理二丛吐丛二+ h‘ U~丰I一U，_I_ +尸(x们厂竺二兹巴几十，(x功)u朋一o作二阶精度逼近，其中网格几。和几;由点x.“。h组成(m是一整数)，“.是函数u*在点x.的值.又，方程 au aZu L“三共牛一斗冬二0， --一ar ax，可用关于光滑解的两种不同的差分近似来逼近: _.月+1_”月气.月上.” 一门、“nt4用“用十l‘“阴l“用一I八 于九‘(撇式格式(exPlie，}seheme))和! “几’l一嗽试，‘l}一翔二，曰衅，‘从 拭’价二一一-一—一了一--一一几，(隐式格式(一mf)liczt scheme))，其中网格D*。和D*:由点(x。，甲=(川入，似)组成，:二rhZ，r二常数，巾和n是整数，。二是函数翻、在网格点(x，，t。)的值.存在这样的有限差分算子L，它对微分算子L的逼近，仅关于方程L。一0的解。特别好，而关于其他函数则差一些.例如，算一子L*L*U。三兴，·卜·夸卫一尹{刁内队引〔其中汀二·。州一随甲‘气))关f任意的光滑函数。(*)是算 广L- d仪 L“一…一甲〔戈，“)Z(工) 办的一阶逼近(_关于八)、而关于方程大u=O的解却是二阶逼近(假定函数:，充分光滑)在利用有限差分方程与。。
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