【摘要】 <正> 1987年,李寿佛针对RKMs求解Hilbert空间中的K类初值问题建立了（θ,p,q）-代数稳定性准则。本文试图对此准则作适当扩充使其适合于求解Hilbert空间中的K^p类IVPs的含高阶导数的RKMs。为此,本文第二节给出了K^p类IVPs的某些性质;第三节建更多还原

【Abstract】 In this paper, the theory on (0, p, q)-algebraic stability of Runge-Kutta methods (RKMs) for the initial value problems (IVPs) of the class K0.t in a Hilbert space, which was presented by Li shoufu in 1987, is generalized. We establish the concept of (θ,α, β)-algebraic stability of RKMs with higher derivatives for the IVPs of the class K(P)σ,τ in a Hilbert space. It is shown that a (θ,α,β)-algebraically stable RKM with higher derivatives is necessarily ( 1-()转换成multiply from i=1 to s ()θi,α,β)-algebraically stable, therefore it is ( 1 -()转换成multiply from i=1 to s ()θi,α,β)) -stable.更多还原