Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:85

Article

Zhang, CJ ; Zhou, SZ

关键词: strong algebraic stability;    GDN-stability;    D-convergence;    DDE;    Runge-Kutta method;   

DOI  :  10.1016/S0377-0427(97)00118-0

来源: Elsevier

【 摘 要 】

This paper deals with the stability and convergence of Runge-Kutta methods with the Lagrangian interpolation (RKLMs) for nonlinear delay differntial equations (DDEs). Some new concepts, such as strong algebraic stability, GDN-stability and D-convergence, are introduced. We show that strong algebraic stability of a RKM for ODEs implies GDN-stability of the corresponding RKLM for DDEs, and that a strongly algebraically stable and diagonally stable RKM with order p, together with a Lagrangian interpolation of order q, leads a D-convergent RKLM of order min{p, q + 1}.

【 授权许可】

Free