H-stability of linear theta-method with general variable stepsize for system of pantograph equations with two delay terms

This paper deals with H-stability of the linear @q-method with a general variable stepsize for the system of pantograph equations with two delay terms. A sufficient condition such that the system of pantograph equations is asymptotically stable is derived. Furthermore, when the linear @q-method with a general variable stepsize is applied to this system, it is shown that the linear @q-method is H-stable if and only if 1/2<@q=<1.

[1]  Yunkang Liu,et al.  On the t-method for delay differential equations with infinite lag , 1996 .

[2]  A. Iserles,et al.  Stability of the discretized pantograph differential equation , 1993 .

[3]  K. J. in 't Hout,et al.  A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations , 1992 .

[4]  M. N. Spijker,et al.  The stability of the θ-methods in the numerical solution of delay differential equations , 1990 .

[5]  Lianhua Lu,et al.  Numerical stability of the t-methods for systems of differential equations with several delay terms , 1991 .

[6]  J. In 'T Houtk,et al.  Stability analysis of Runge-Kutta methods for systems of delay differential equations , 1997 .

[7]  Toshiyuki Koto,et al.  Stability of Runge-Kutta methods for the generalized pantograph equation , 1999, Numerische Mathematik.

[8]  Yunkang Li,et al.  Stability analysis of $\theta$ -methods for neutral functional-differential equations , 1995 .

[9]  Yunkang Liu,et al.  Numerical investigation of the pantograph equation , 1997 .

[10]  K. J. in 't Hout,et al.  On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations , 1996 .

[11]  Nicola Guglielmi,et al.  On the Contractivity and Asymptotic Stability of Systems of Delay Differential Equations of Neutral Type , 1999 .

[12]  Y. Kuang,et al.  Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag , 1990 .

[13]  M. Calvo,et al.  On the asymptotic stability ofθ-methods for delay differential equations , 1989 .

[14]  Arieh Iserles,et al.  On the generalized pantograph functional-differential equation , 1993, European Journal of Applied Mathematics.

[15]  A. Iserles.  University of Cambridge Exact and Discretized Stability of the Pantograph Equation Arieh Iserles Exact and Discretized Stability of the Pantograph Equation , 1996 .

[16]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[17]  A. Iserles,et al.  On the dynamics of a discretized neutral equation , 1992 .

[18]  L. Torelli,et al.  Stability of numerical methods for delay differential equations , 1989 .

[19]  Nicola Guglielmi,et al.  Asymptotic stability properties of T-methods for the pantographs equation , 1997 .

[20]  M. N. Spijker,et al.  Stability analysis of numerical methods for delay differential equations , 1991 .

[21]  Yunkang Liu,et al.  Asymptotic behaviour of functional-differential equations with proportional time delays , 1996, European Journal of Applied Mathematics.