一种求解常微分方程初值问题的单步法  

A Class of Step Method for Solving Initial Value Problems of Ordinary Differential Equations

作　　者：靳绍礼[1] 李体云[1] 宋玉成[1] 

机构地区：[1]济南大学理学院,济南250022

出　　处：《科学技术与工程》2010年第31期7695-7698,共4页Science Technology and Engineering

基　　金：中国教育部博士基金(XBS09239)资助

摘　　要：利用Cotes求积公式推出求解常微分方程初值问题的5点6阶方法,进而用Newton-Cotes求积公式,推出了求解常微分方程初值问题的更为一般的公式,并给出了相应方法的绝对稳定区间。最后通过数值算例表明,该方法具有一定的优势。With Cotes-integration,a class of one step method is got for solving initial value of ordinary differential equations,which is 5 point 6 order method,then with Newton-Cotes-integration.A general method for solving initial value of orinary differential equations is got.At the same time,the corresponding mentods＇absolute stability is got.Numerical tests show that these methods are efficient.

关 键 词：一阶常微分方程 单步方法 Cotes求积公式 绝对稳定 相容阶 

分 类 号：O175.1[理学—数学]