奇异两点边值问题改进的梯形公式外推方法  

Extrapolation of modified trapezoidal rule for a class of singular two-point boundary value problems

作　　者：唐永超[1] 王同科[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2015年第4期5-7,19,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11471166)

摘　　要：研究奇异两点边值问题的高精度数值方法.首先,将奇异两点边值问题转化为奇异积分的计算问题.其次,利用改进的复合梯形公式离散奇异积分,针对几种不同情形给出了误差渐近展开式.再次,由误差估计式设计了一种改进的龙贝格算法,利用该算法可以得到问题的高精度数值解.最后,通过数值算例说明了算法的有效性.High precision numerical method for singular two-point boundary value problems （SBVPs） is studied. Firstly, the SBVPs are transformed into the computation of singular integrals. Secondly, the singular integrals are discretized by modi- fied composite trapezoidal rule and the error asymptotic expansions are obtained for some kind of cases. Thirdly, a modified Romberg extrapolation algorithm is designed to obtain high precision numerical results based on the error expansions. Fi- nally, numerical examples show the effectiveness of the algorithm.

关 键 词：奇异两点边值问题 复合梯形积分公式 分数阶泰勒展开式 误差渐近展开 龙贝格算法 

分 类 号：O241.82[理学—计算数学]