【摘要】 研究一类积分微分方程多步Runge-Kutta方法的散逸性.利用复合求积公式逼近积分项,当k≤1时,证明了(k,l)-代数稳定的、不可约的多步Runge-Kutta方法的有限维散逸性.此外,当k<1时,得到了该方法的无限维散逸性结果.这些结果表明所考虑的数值方法很好地继承了系统本身所具有的散逸性,丰富了数值求解这一类积分微分方程的方法.更多还原

【Abstract】 This paper is concerned with the dissipativity of multistep Runge-Kutta methods for one kind of integro-differential equations.When the integration term is approximated by the compound quadrature formula,it is proved that a(k,l)-algebraically stable,irreducible multistep Runge-Kutta method is dissipative for finite-dimentional dynamical systems when k≤1.In addition,we obtain dissipativity results of this method for infinite-dimentional dynamical systems when k<1.The results show that the multistep Runge-Kutta methods inherit the important property of the underlying systems,and enrich the numerical methods for us to solve the underlying systems.更多还原