The Stability Analysis Of Numerical Methods For Volterra Functional Differential Equations

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,β}f:[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.