非线性Volterra延迟积分微分方程Runge-Kutta方法的散逸性

Dissipativity of Runge-Kutta method for nonlinear Volterra delay-integral-differential equations

考虑了非线性Volterra延迟积分微分方程Runge-Kutt方法的散逸性.当积分用PQ求积公式逼近时,得到了(k,l)-代数稳定的Runge-Kutt方法的散逸性;证明了:代数稳定且DJ-不可约的Runge-Kutt方法是有限维散逸的;当k<1时,(k,l)-代数稳定的Runge-Kutt方法是无限维散逸的.

The dissipativity of Runge-Kutta method nonlinear Volterra delay-integral-differential equations is discussed.The dissipativity of（k,l）-algebraically stable Runge Kutta method is discussed when the intergration term is approximated by PQ formula.It is proved that an algebraically stable and DJ-irreducible Runge-Kutta method is dissipative for finite dimensional dynamical systems,a（k,l）-algebraically stable Runge-Kutta method is dissipative for infinite dimensional systems if k〈1.