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1、2011–4–20StabilityAnalysisofOne-legMethodsforFunctionalDifferentialandFunctionalEquationsCandidateSupervisorCollegeProgramHuangFenglingProfessorYuYuexinMathematicsandComputationalScienceComputationalMathematicsSpecializationDegreeUniversityDateTheoryandApplicationofN
2、umericalMethodsforStiffDifferentialEquationsMasterofScienceXiangtanUniversityApril20,2011,.,,..,:A-,A-,2,,:,G(c,p,q)-.,.D(α,β1,β2,σ,γ1,γ2,δ),G(c,p,q)-.,.,,.G(c,p,q)-.IAbstractFunctionaldifferentialandfunctionalequations(FDFEs)areaclassofhy-birdprobl
3、emthatareformedbyfunctionaldifferentialequationsandfunctionalequations.Theclassofhybirdproblemarisewidelyinthefieldsofscienceandengineering.Itismeaningfultoinvestigatethetheoryandapplicationofnumer-icalmethodsforFDFEs.Duetothecomplexityoftheproblem,theasymptoticstabilit
4、yofnumericalmethodsforlinearFDFEshasbeendiscussedbyseveralauthors.Recently,Yuetal.investigatedthestabilityoftheproblemitselfandthenumericalstabilityofone-legmethods.ItisprovedthatanyA-stableone-legmethodscanpreservethestabilityoftheproblem.However,thehighestconver-gen
5、ceorderisonly2oftheA-stableone-legmethods.Itmakesmanycommonhigher-orderone-legmethodsnotincluded.Forthesereasons,thepresentpa-perfurtherstudythenumericalstabilityofG(c,p,q)-algebraicallystableone-legmethods.Themainresultsofthispaperareasfollows.Firstly,weintroducethec
6、lassofD(α,β1,β2,σ,γ1,γ2,δ)andderivethestabilityconditionoftheproblem.Sec-ondly,one-legmethodsareappliedforsolvingthehybirdproblem.ThestabilityandasymptoticstabilityconditionsoftheG(c,p,q)-algebraicallystableone-legmethodsareobtained.Finally,thenumericalexperimentsareg
7、iventodemon-stratethetheoreticalresults.KeywordFunctionaldifferentialandfunctionalequations;Stability;Asymp-toticstability;One-legmethods;G(c,p,q)-algebraicallystable.II.........................................................1..........................................
8、....7§2.1D(α,β1,β2,σ,γ1,γ2,δ)......................................7§2.2§3.1§3.2§3.3......................................
