一類剛性非自治系統(tǒng)的組合解法.pdf

1、華東師范大學(xué)碩士學(xué)位論文一類剛性非自治系統(tǒng)的組合解法姓名：丁新濤申請學(xué)位級別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：陳果良20050501ABSTRACTStiffdifferencialequations(SDE)alwayshaveit’sapplicationsinhigh—techscopes，likeaviation，thermicnuclearreaction，automaticcontroltelectronicnetwork＆ch

2、emicaldynamicsetc，whichhavegreatimportancetodowithnationaldefenceandmodernizationconstructionSo，itgoeswithoutsayingtobeveryimportantBeendiscretedbyspacevariable，partialdifferencialequation(PDE)withinitialvalueorborderval

3、ue_wanldbeconvertedtobigscaleordanarydifferencialequations(ODE)anditisa丑importantheadspringthatcausesstiffproblemForlinearstiffproblem，themaintheoryhaveA—stability(Dahlquist，1963)，A(n)一stability(Wtdlund，1967】andstiffstab

4、ility(Gear，19fi9)ThereweremanydemesticscholarsearchedlineartheoryincludingJiaoxunKuang，GuoliangChen，JiaxiangXiang，ShoufoLi，ChenmingHuang，QingyangLi，JinggaiTesearchfornonlinearstiffproblemButcher＆BurrageestablishedB—stabl

5、eandalgebrastabletheoryforRungeKuttamethodfrom19751979(see[17][191121～23】甙c)Frank，Schneid＆UeberhuberestablishedBconvergcucetheoryforRnageKuttamethodfrom1981—1985(see[14][15]etc)Atthesametime，thereacemanydemcsticscholarde

6、dicatetoBtherom(see[8^一lO]etc)Buttheresearchaboutconvergenceofnonlinearstiffproblemdido’tre％hidealaimthatcanbeanalysedtorationconvergenceInrecentyearspeoplepayattentiontoextensiveordinarymultivaluemethodsmoreandmoreMixme

7、thodisoHeofpopularmethodinrecentyearsAndtoenhancecalculationspeedofstiffsystem，manyscholaruseparallelmethed(seef2】f9]f20]etc)Merson，Butcher，Hairer＆Wanneretcinventedroottreetheory(see[41[5][filetc)Justfromroottreetheorymi

8、xmethodandparallelmethodthispapergivescombinedRKRosenbrochmethod，whichcanparallelrealizeacertainstiffnonantonomysystemnumericalsolutionThisPaDel“isthedevelopmentofRKRosenbrockmethodofprofessorChenLirongTherearesomedetail

9、saboutcombinedRKR06enbrockmethodofstiffautonomylargesysteminbibliography【11121【3】Thefirstpartofthispaperisgoingtointroduceroottreetheoryofforerunners；ThesecondpartisgoingtogivecombinedRKRosonbrockmethodenddiscussit’srank

10、condition；ThethirdpartofthispaperwillcheckAstableconditionsofthestiffpartinequationsystem；Thefourthpartwillgiveconvergencetheormandstabilizationtheorm；Thefifthpartwillgiveonenumericalexample，calculatedresultandtheresulta