Volterra泛函微分方程數(shù)值方法的穩(wěn)定性分析.pdf

1、湘潭大學(xué)碩士學(xué)位論文Volterra泛函微分方程數(shù)值方法的穩(wěn)定性分析姓名：王炳濤申請學(xué)位級別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：文立平20080520ABSTRACTIn this paper, we generalize the initial value problem class of ordinary differ-ential equations Kσ,τ (given by S.F. Li in 1987) and corresp

2、onding problem classof delay differential equations (given by C.M. Huang in 2002 BIT) to the generalinitial value problem class of Volterra functional differential equations Kσ,τ,β ? ??y′(t) = f(t, y(t), y(·)), t ∈

3、[0, T]y(t) = ?(t), t ∈ [?d, 0],f : [0, T] × Rm × Cm[?d, T] → Rm satisfying the condition2Re?u?v, f(t, u, ψ1(·))?f(t, v, ψ2(·))? ≤ σ?u?v?2+τ?f(t, u, ψ1(·))?f(t, v, ψ2(·))?2+β max ?d≤ξ≤t ?ψ1(ξ

4、) ? ψ2(ξ)?2, ?t ∈ [0, T], u, v ∈ Rm, ψ1, ψ2 ∈ Cm[?d, T].Solving the problem class Kσ,τ,β by (θ, p, q)-algebraically stable Runge-Kutta meth-ods and (k, p, q)-algebraically stable general linear methods, we obtain the sta

5、bilityresults of these methods. These results can be regarded as extension of the stabil-ity results of corresponding numerical methods for ordinary differential equationsand delay differential equations as well as exten

6、sion of corresponding results forVolterra functional differential equations(obtained by S.F. Li in 2003 and 2005).Even though for delay differential equations which is special functional differentialequations, our result

7、s are more comprehensive and profound than the results whichhave been existent.Keywords: Volterra functional differential equations; (θ, p, q)-algebraically stable;(k, p, q)-algebraically stable; general linear method; R