AN ANALYTICAL-NUMERICAL METHOD FOR A TYPICAL BIFURCATION PROBLEM

In this paper, the nonlinear two-point boundary vslue problem which has a secondary bifurcation point is solved by an anlyticnumerical mechod.The problem was first transformed analytically into finding roots of the trascendental equation Then the turning point was obtained numerically, λ_c=1.87452030182. And the following three cases are all considered: the problem has two solutions, one solution or no solution, when λ<λ_c, λ=λ_c, or λ>λ_c, respectively.The steps for solving the problem and some results of numerical experiments are given in the paper.     

对称区域分裂法解一类交接面问题

本文考察用对称区域分裂法来解比较一般的“对称”交接面问题,而以普通的偏微分方程边值问题作为它的特例.文中提供了三种算法,包括改进的区域分裂法.运用这些算法,原问题可化为两个或四个具半规模的子问题,而各子问题不再是具有奇异性的交接面问题.所有算法均可在多机(multiprocessor及multicomputer)上完全并行,且通讯量极少.文末给出了三种算法的数值试验结果.