Volterra泛函微分方程數(shù)值方法的散逸性.pdf

1、湘潭大學(xué)碩士學(xué)位論文Volterra泛函微分方程數(shù)值方法的散逸性姓名：劉學(xué)泳申請學(xué)位級別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：文立平20070422IIAbstractVolterrafunctionaldifferentialequations(VFDEs)arisewidelyinthefieldsofbiologyeconomicsphysicschemistryengineeringcontroltheysoon.Itismeaning

2、fultoinvestigatethetheyapplicationofnumericalmethodsfVFDEs.Manydynamicalsystemsareacterizedbythepropertyofpossessingaboundedabsbingsetwhichalltrajectiesenterinafinitetimethereafterremaininside.Whenconsideringtheapplicabi

3、lityofnumericalmethodsfthesesystemsitisimptanttoanalyewhethernotnumericalmethodsinheritthedissipativityoftheunderlyingsystem.Thispaperdealswiththeanalyticnumericaldissipativityoffollowingsystem:???≤≤?=≥?=′0)()(0))()(()(t

4、ttytytytftyτ?(1)wherethefunctionalfsatisfiesthat)[0)(max)()()())((Re22∞?∈∈≥?≤???≤≤?τ?ξ?βαγ?ξτXttCXuttuttutfu(2)Themainresultsinthispaperareasfollows:1.Weobtaintheanalyticdissipativityresultof(1):When000εthereexistsaposit

5、ivenumber20)(sup)(tttt??ε?τ≤≤??==suchthatεβαγ?ttwhere)(sup)(sup)(sup000000ttttttγγββαα≥≥≥===。2.Weinvestigatethedissipativityofθmethodsf(1)obtainthedissipativityresultsofonelaglinearθmethods.3.Weinvestigatethedissipativit

6、yofBDFmethodsf(1)obtainthedissipativityresultsofBDFmethods.4.SeveralnumericalexamplesinwhichtheθmethodsBDFmethodsareappliedrespectivelyaregiventoconfirmtheeticalresultspresentedinthispaper.Keywds:Volterrafunctionaldiffer