[1] |
Temam R. Infinite-dimensional dynamical systems in mechanics and physics[M]. New York: Springer-Verleg, 1997: 68.
|
[2] |
Hill A T. Dissipativity of Runge-Kutta methods in Hilbert spaces[J]. BIT Numerical Mathematics, 1997,37:37-42.
|
[3] |
Humphries A R, Stuart A M. Runge-Kutta methods for dissipative and gradient dynamical systems[J]. SIAM Journal on Numerical Analysis, 1994,31(5):1452-1485.
|
[4] |
Huang C M, Chang Q S. Dissipativity of multistep Runge-Kutta methods for dynamical systems with delays[J]. Mathematical and Computer Modelling, 2004,40(11/12):1285-1296.
|
[5] |
Wang S X, Wen L P. Numerical dissipativity of neutral integro-differential equations with delay[J]. International Journal of Computer Mathematics, 2017,94(3):536-553.
|
[6] |
Wen L P, Wang W S, Yu Y X. Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations[J]. Nonlinear Analysis-theory Methods and Applications, 2010,72(3/4):1746-1754.
|
[7] |
Liu X Y, Wen L P. Dissipativity of one-leg methods for neutral delay integro-differential equations[J]. Computers and Mathematics with Applications, 2010,235(1):165-173.
|
[8] |
Qi R, Zhang C, Zhang Y. Dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations[J]. Acta Mathematicae Applicatae Sinica (English Series), 2012,28(2):225-236.
|
[9] |
Gan S Q. Dissipativity of the backward Euler method for nonlinear Volterra functional differential equations in Banach space[J]. Advances in Difference Equations, 2015. DOI: 10.1186/s13662-015-0469-8.
doi: 10.1186/s13662-016-0991-3
pmid: 27818676
|
[10] |
Wang W S. Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations[J]. Computers and Mathematics with Applications, 2017,309(1):132-144.
|
[11] |
Wang W S, Zhang C J. Analytical and numerical dissipativity for nonlinear generalized pantograph equations[J]. Discrete and Continuous Dynamical Systems, 2011,29(3):1245-1260.
|
[12] |
Zhang C J, Qin T T. The mixed Runge-Kutta methods for a class of nonlinear functional-integro-differential equations[J]. Computers and Mathematics with Applications, 2014,237(15):396-404.
|
[13] |
Qin T T, Zhang C J. Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations[J]. Computers and Mathematics with Applications, 2015,250(1):47-57.
|
[14] |
Wen L P, Liao Q. Dissipativity of one-leg methods for a class of nonlinear functional-integro-differential equations[J]. Computers and Mathematics with Applications, 2017,318:26-37.
|
[15] |
Liao Q, Wen L P. Dissipativity of Runge-Kutta methods for a class of nonlinear functional-integro-differential equations[J]. Advances in Difference Equations, 2017. DOI: 10.1186/s13662-017-1196-0.
doi: 10.1186/s13662-016-0991-3
pmid: 27818676
|
[16] |
Huang C M, Chang Q S. Dissipativity of multistep Runge-Kutta methods for dynamical systems with delays[J]. Mathematical and Computer Modelling, 2004,40(11/12):1285-1296.
|
[17] |
Burrage K, Butcher J C. Non-linear stability of a general class of differential equation methods[J]. BIT, 1980,20(2):185-203.
doi: 10.1007/BF01933191
|