|
|||||
|
|
The stability of modified Runge-Kutta methods for the pantograph equation |
|
| Authors: | M Z Liu Z W Yang Y Xu |
| Institution: | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China ; Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China Y. Xu ; Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China |
| Abstract: | In the present paper, the modified Runge-Kutta method is constructed, and it is proved that the modified Runge-Kutta method preserves the order of accuracy of the original one. The necessary and sufficient conditions under which the modified Runge-Kutta methods with the variable mesh are asymptotically stable are given. As a result, the  -methods with  , the odd stage Gauss-Legendre methods and the even stage Lobatto IIIA and IIIB methods are asymptotically stable. Some experiments are given. |
| Keywords: | Pantograph equation asymptotical stability Runge-Kutta methods |
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 | |
| 点击此处可从《Mathematics of Computation》下载免费的PDF全文 | |