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1)  hyperasymptotic expansions
超渐近展开
2)  asymptotic expansion
渐近展开
1.
An asymptotic expansion formula of Sikkema operators on the simplex;
单纯形上Sikkema算子的一种渐近展开公式
2.
By introducing extended variables and using the theory of differential inequality,the uniformly effective asymptotic expansion is obtained under appropriate conditions.
文中揭示了其解呈现双重层性质,即奇摄动问题的解在该区域内呈现不同“厚度”的初始层性质;在适当的假设条件下,通过引进不同量级的伸长变量,构造不同“厚度”的初始层校正项,并利用微分不等式理论,得到了解的任意次近似的一致有效的渐近展开式。
3.
The asymptotic expansion term of remainder term for error of inequality distance first kind cubic spline interpolating function is advanced using interpolation method for basic spline.
利用基样条插值方法,给出非等距三次样条(Ⅰ)型插值函数余项渐近展开式。
3)  asymptotic expansions
渐近展开
1.
For the elliptic partial differential equations of variable coefficient,we obtain the product theorem of asymptotic expansions of energy integral as follows:B(w,v_h)=∑ni=1h~(2i)_e∫_ΩF_i(D~(2i-2)_x(v_(xx)φ))v_hdxdy+∑nj=1k~(2j)_e∫_ΩG_j(D~(2j-2)_y(u_(yy)φ))u_hdxdy+∑ni+j=2h~(2i)_ek~(2j)_e∫_Ω[F_(ij)(D~(2i-2)_xD~(2j)_y(u_(xx)φ))+G_(ij)(D~(2i)_xD~(2j-2)_y(u_(yy)φ))]v_hdxdy+R_(n,h).
针对变系数椭圆型方程矩形元,证明了能量积分的渐近展开具有如下的乘积定理:∫Ω∫Ωk2jh2iFi(D2i-2Gj(D2j-2B(w,uh)=∑ny(uyyφ))vhdxdy+ex(uxxφ))vhdxdy+∑nei=1j=1∫Ω∑nh2i[Fij(D2i-2eek2jxD2j-2y(uyyφ))]vhdxdy+Rn,h。
2.
An analysis of asymptotic expansions of iterated Galerkin methods for eigenvalue problems of the second kind Fredholm integral equations is presented.
讨论了第二类 Fredholm积分方程特征值问题迭代 Galerkin方法的渐近展开 ,并在此基础上分析了Richardson外推方法。
3.
In this paper,we obtained item-by-item asymptotic expansions of two kind quadratic spline interpolation.
本文给出了二次样条在两类端点条件下插值误差的逐项渐近展开结果,从而获得插值误差关于步长h的级数表示式。
4)  asymptotically developable method
渐近展开法
5)  asymptotic expansion
渐近展开式
1.
By using the Lindatedt-Poincare method,introducing the transformation of parameter and eliminating the secular terms in the formal solution,the first order uniformly valid asymptotic expansion is obtained.
讨论了一类二阶弱非线性常微分方程,利用Lindstedt-Poincare法,引入参量变换,消去形式解中出现的长期项,得到了解的一阶一致有效的渐近展开式。
2.
In this paper,the author discusses the multi-layer solution with two special limits in boundary layer of the singularly perturly boundary value problem and obtains uniformly valid zero order asymptotic expansion by using the matching asymptotic expanding method.
利用匹配渐近展开法 ,讨论了奇摄动边值问题中边界层内存在有两个特异极限的多层解 ,得出了奇摄动边值问题的一致有效的零次渐近展开
3.
Under a given assumption, the author of this paper obtained the uniformly powerful asymptotic expansion of M order and made an estimation of the remainder in asymptotic series.
研究拟线性双曲型方程柯西问题,在一定假设下,得到解的M阶一致有效的渐近展开式,并作出余项估计。
6)  asymptotic expansions
渐近展开式
1.
In this paperFwe study thesingular perturbation of nonlinear ddifferential equations with two parameters:y = f(x,y, z, ε,μ),y(1,ε,μ) = a(ε,μ)εy" = F(x,y, z, z_1, ε,μ), z (0,ε,μ) = b(ε,μ)z(1,ε,μ) = c(ε,μ)Under some affropriate conditions, using the theory of differential inequalities, we qet the existence of the solution and its asymptotic expansions which is uniformly valid for all orders unti
本文研究一类含有双参数非线性微分方程组的奇摄动,在适当的假设条件下,利用微分不等式理论,证明了摄动解的存在,并给出了解的直到o(sum from k=0 to n+1 ε~(N+1-K)μ~k)阶的一致有效渐近展开式。
2.
My method is to find the new equations and its solutions from the known equations and its solutions,and to find the asymptotic expansions.
给出一类二阶线性方程的求解公式和解的渐近展开式。
补充资料:渐近展开


渐近展开
asymptotic expansion

  渐近展开【as州p咖ce习娜nsi.;~价..幻以犯脚冬~e皿e1,函数f(x)的 一个级数: 艺么(x) 月二0对于任何整数N)0,都有 刀 f(x)=艺么(x)+o(卿(x))(x*x。),(l) ”=0其中{叭(x)}是某一给定的(当x~x。时的)渐近序列(asymPtotic seq~ce).在这种情况下,还可表示为 f(x)~叉华。(x),f叭(x)},(x*x。).(” n二0如果由上下文显然可知{叭(x)}指的是什么序列,则在式(2)中可以省去这个序列. 渐近展开(2)称为E咖lyi意义下的渐近展开(as ym-ptotie ex稗nsion in the sense of Erd‘l功)([3]).形女口 f(x)一艺an叭(x)(x*x。)(3) 月二0的展开(其中a。都是常数),称为几inca记拿冬丁的渐近展开(asyn叩幻tic exPansion in the sense of Poi仆ca始).当给定渐近函数序列{叭(x》时,则与渐近展开(2)不同,渐近展开(3)可由函数f(x)本身唯一确定.如果对于有限个值N=O,…,N0<的,式(l)都成立,则这个展开称为精确到。伸屿(x》的渐近展开·级数 艺么(x),艺a。气(x) 月=on二0称为渐近级数(asymPtotic series).这样的级数通常是发散的,其中最常应用的是渐近幕级数(asymPtoticpo从吧r series);对应的渐近展开是Poinca比意义下的渐近展开. 下面是Erd‘lyi意义下的渐近展开的一个例子:_厂了一’{{二,二{石““’一V认{“05汗万一刘户仁一‘”“2一‘一‘ 」二。二}石、.} 一sln‘万一蕊一}户{’“2·’一‘一‘{(*,+£)、其‘,j是Besse!函数,l6J r(歹、n十l一厂2) ‘月’l气F一刀,I,‘, 函数的渐近昵环和渐近级数的概念,是H.Poln-以re(!ID在研究大体力学问题时引人的.渐近展汗的些特例旱在18担一纪时就已被发现和使用(「2j).渐近展汗在许多数学、力学和物理学问题中起着重要作用这是因为许多问题不能精确求解,但是它们的解可以作为渐近近似而得到此外,在渐近展开比较容易求得时,往往可以不必采川数值方法.
  
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