摘要
本文讨论如下形式的二阶微分方程y″（x）＋P（x）y′（x）＋Q（x）y（x）=R（x），0＜x＜1，y′（0）＝A，y（1）＝B，其中A，B为常数，系数P（x），Q（x）在x=0处有奇性。考虑到系数在x=0处有奇性，无法用一般差分格式进行计算，故将区间（0，1]划分成（0，δ]和[δ，1]，（δ靠近奇点）。在（0，δ]区间寻求级数形式的解，继而确定y（δ）值。在[δ，1]区间上用离散不变嵌入法寻求该问题的差分格式，并给出了离散形式下解yi的计数步骤，最后给出数值例子并与真解进行了比较，得到了结点误差|yi－y（xi）|≤10－4。
In this paper, the second order ordinary differential equation y″(x) +P(x)y′(x) +Q (x)y (x) = R (x), with singularity at x=0 is discussed, and 0<x<1, y′(0) = A,y(1 ) = B within the above, A and B are constant, and P(x),Q(x) as coefficient. Ordinary difference scheme can not be used for solving this kind of problem. So the interval (0, 1] is divided into two parts (0,δ] and [δ, 1], and δ is near the singularity. By employing the series expansion on the interval (0,δ], y(δ) is obtained, then the discrete invariant imbedding method is described to solve the problem over the reduced interval [δ, 1]. Finally a numerical example is given and compared with the precision solution, and the node error|yi-y(xi)|≤10-4 is gained.
出处
《上海水产大学学报》
CSCD
1998年第3期206-210,共5页
Journal of Shanghai Fisheries University
关键词
离散不变嵌入法
奇异边值问题
二阶
常微分方程
singular boundary condition, discrete invariant imbedding method, iterative method, node error
