【作者】 王炳涛；

【导师】 文立平；

【作者基本信息】 湘潭大学 ， 计算数学， 2008， 硕士

【摘要】 本文将常微分方程初值问题类K_σ,τ（李寿佛1987年提出）及相应的延迟微分方程初值问题类（黄乘明2002年BIT）进一步拓广到一般的Volterra泛函微分方程初值问题类K_σ,τ,β：其中f：[0，T]×R^m×C_m[-d，T]→R^m满足条件：将（θ，p，q）-代数稳定的Runge-Kutta方法及（k，p，q）-代数稳定的一般线性方法应用于K_σ,τ,β类问题，获得了这些方法的稳定性结果．这些结果可视为常微分方程及延迟微分方程相应数值方法稳定性结果的推广和发展，也可视为Volterra泛函微分方程相应结果（李寿佛2003年和2005年获得）的进一步推广．即使对于延迟微分方程这种特殊的泛函微分方程，我们的结果比文献中已有的结果更加广泛和深刻．更多还原

【Abstract】 In this paper, we generalize the initial value problem class of ordinary differentialequations K_σ,τ（given by S.F. Li in 1987） and corresponding problem class of delay differential equations （given by CM. Huang in 2002 BIT） to the general initial value problem class of Volterra functional differential equations K_σ,τ,βf:[0,T]×R^m×C_m[-d,T]→R^m satisfying the conditionSolving the problem class K_σ,τ,β by （θ,p, g）-algebraically stable Runge-Kutta methodsand （k, p,q）-algebraically stable general linear methods, we obtain the stability results of these methods. These results can be regarded as extension of the stabilityresults of corresponding numerical methods for ordinary differential equations and delay differential equations as well as extension of corresponding results for Volterra functional differential equations （obtained by S.F. Li in 2003 and 2005）. Even though for delay differential equations which is special functional differential equations, our results are more comprehensive and profound than the results which have been existent.更多还原