Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations

This paper deals with the stability of Runge-Kutta methods for a class of stiff systems of nonlinear Volterra delay-integro-differential equations. Two classes of methods are considered: Runge-Kutta methods extended with a compound quadrature rule, and Runge-Kutta methods extended with a Pouzet type quadrature technique. Global and asymptotic stability criteria for both types of methods are derived.

[1]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[2]  Marino Zennaro,et al.  Strong contractivity properties of numerical methods for ordinary and delay differential equations , 1992 .

[3]  Stefan Vandewalle,et al.  An Analysis of Delay-Dependent Stability for Ordinary and Partial Differential Equations with Fixed and Distributed Delays , 2004, SIAM J. Sci. Comput..

[4]  Marino Zennaro,et al.  Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations , 1997 .

[5]  Neville J. Ford,et al.  Stability properties of a scheme for the approximate solution of a delay-integro-differential equation , 1992 .

[6]  Yuhao Cong,et al.  Stability of numerical methods for delay differential equations = 延时微分方程数值方法的稳定性 , 2005 .

[7]  Neville J. Ford,et al.  Convergence of Linear Multistep Methods for a Class of Delay-Integro-Differential Equations , 1988 .

[8]  A. Bellen,et al.  Numerical methods for delay differential equations , 2003 .

[9]  Chengjian Zhang,et al.  Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization , 2004 .

[10]  Chen Guangnan,et al.  Stability Analysis of Runge-Kutta Methods for Non-Linear Delay Differential Equations , 1999 .

[11]  Christopher T. H. Baker,et al.  A perspective on the numerical treatment of Volterra equations , 2000 .

[12]  H. Brunner,et al.  The numerical solution of Volterra equations , 1988 .

[13]  T. Koto.  Stability of Runge-Kutta methods for delay integro-differential equations , 2002 .

[14]  Dirk Roose,et al.  Computing Stability of Differential Equations with Bounded Distributed Delays , 2003, Numerical Algorithms.