This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, l...This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r（0）-stable methods are found. Later, some examples of r（0）-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10671078)the Program for New Century Excellent Talents in University,the State Education Ministry of China. supported in part by E-Institutes of Shanghai Municipal Education Commission (No.E03004)+3 种基金National Natural Science Foundation of China(No.10671130)Shanghai Science and Technology Commission(No.06JC14092)Shuguang Project of Shanghai Municipal Education Commission(No.06SG45)the Shanghai Leading Academic Discipline Project(No.S30405)
文摘This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r（0）-stable methods are found. Later, some examples of r（0）-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.
