两端边值问题的通用精细积分法  

General Precise Integration Method for Two-point Boundary Value Problems

作　　者：张文志[1] 富明慧[1] 蓝林华[1] 

机构地区：[1]中山大学应用力学与工程系∥广东省近岸海洋工程重点实验室,广东广州510275

出　　处：《中山大学学报（自然科学版）》2010年第6期15-19,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10672194);中俄NSFC-RFBR协议资助项目(10811120012)

摘　　要：提出了常微分方程组边值问题精细积分的一种通用方法。利用传递矩阵建立区段代数方程,并针对各种边界条件,导出了区段合并消元的递推公式。由于直接利用了传递矩阵的结果,其区段合并消元过程具有很高的计算效率。另外文章方法比黎卡提方法更容易处理复杂边界条件,具有广泛的适用性。数值算例证明了文章方法的有效性。A general precise integration method for two-point boundary value problems of ordinary differential equations is presented.Using the transfer matrix,interval algebraic equations are established and the recursive formulas for interval combination and condensation are derived for various boundary conditions.By utilizing the results of the transfer matrix directly,the process of interval combination and condensation has high efficiency.In addition,the present method has wide application for which can deal with various boundary value problems.Numerical examples show the validity of the present method.

关 键 词：一阶常微分方程组 边值问题 精细积分法 病态方程 递推算法 

分 类 号：O241.4[理学—计算数学]