二阶常微分方程 meaning in Chinese
second order ordinary differential equation
Examples
- This paper is concerned with uniqueness of positive solutions to three classes of two - point boundary value problems of ordinary differetial equations . the argument is based on the shooting methord together with the sturm ' s comparison theorem . the main results are as follows : 1
本文运用打靶法及sturm比较定理讨论了三类二阶常微分方程两点边值问题正解的惟一性(如果存在) ，主要结果有：一 - For the class of nonlinear second order ordinary differential equations ( odes ) , we firstly consider one of their special one - dimensional forms , and then prove the existence of solution to its two - point boundary value problem in the light of prior estimate and schauder fixed point theorem . we also show the exact solutions for the special equations as an example and plot the numerical solutions by mathematica
对于这类非线性的二阶常微分方程，我们首先考虑其一维的特殊的形式，运用先验估计，进而利用schauder不动点定理，证明了其两点边值问题解的存在性，并给出具体方程的解作为例子，然后用mathematica作出数值解的图。 - This paper is divided into two sections : section 1 : in ref [ 1 ] , 2 - order ordinary differential initial value problems have the following the superconvergence results and the two - point boundary value problems with singular coefficients have the following the superconvergence results therefore , we have convergence results at the nodes of the linear interpolation for 2 - order ordinary differential initial value problems with singular coefficients section 2 : in ref [ 13 ] , the intensity ( e ) of the electric field in the emission of laser satisfies the nonlinear schrodinger equation it changes to ( 0 . 1 . 4 ) with the 2 - order ordinary differential problem with singular coefficients through evolution and by using the special solution in this paper , we only discuss the 2 - order ordinary differential initial value problems with singular coefficients
本文主要讨论了带奇异系数的二阶常微分方程初值问题的有限元解，并在此基础上研究了激光传输孤波初态的数值模拟。本文分成两部分：第一部分：在文献[ 1 ]中描述了二阶常微分方程初值问题的超收敛结果和带奇异系数的两点边值问题的超收敛结果在此基础上，我们得到了带奇异系数的二阶常微分方程初值问题在节点处线性插值时的有限元解的收敛性第二部分：在文献[ 13 ]中提出了激光的发射机理，其中它的电场强度