一类k步k+2阶解刚性微分方程的混杂法

一类k步k+2阶解刚性微分方程的混杂法 A Class of k-step （k+2） Order Hybrid Methods for Solving Problems of Stiff ODEs 李亮 LI Liang 1 first-author 武汉大学数学与计算机科学学院,武汉,430072 武汉大学数学与计算机科学学院,武汉,430072 College of Mathematics and Computer Science,Wuhan University College of Mathematics and Computer Science,Wuhan University 构造了一类带参数的ｋ步ｋ＋２阶混杂方法，讨论了该方法的稳定性质，并给出了与其等价的二阶导数方法．数值实例说明，这类方法更适合求解非线性Ｓｔｉｆｆ问题，对高震荡问题亦会更有效． In this paper,a class of k-step, （k+2）-st order hybrid method for solving problems of stiff ODEs is constructed and its stability properties are discussed. The methods are proved to be A-stable for k = 1, 2 and stiffly stable for k=4, ..., 8. In implementation by Newton iteration, our methods are more efficient for solving non-linear stiff problems. Finally, some numerical results are presented. 混杂法 stiff-稳定 A-稳定性 hybrid method stiff problem A-stability 10.14188/j.1671-8836.2000.01.005 O241 2000-01-01 2021-04-01 1