二維Burgers方程和帶擴(kuò)散項(xiàng)的色散方程的并行算法.pdf

1、南京航空航天大學(xué)碩士學(xué)位論文二維Burgers方程和帶擴(kuò)散項(xiàng)的色散方程的并行算法姓名：劉宗偉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：張魯明20070101二維Burgers方程和帶擴(kuò)散項(xiàng)的色散方程的并行算法iiABSTRACTInthispaperthefinitedifferencemethodftheinitialboundaryproblemoftheBurgersequationsintwospacedimensionsisc

2、onsidered.Theequationsaredecomposedintotwoonedimensionalequationsbythefractionalstepmethodsthenumericalsolutionfromnthtimelevelto(1)nthtimeleveliscomputedbytwosteps.Firstlytwoasymmetricdifferenceschemesareproposedanalter

3、natinggroupexplicitmethod(AGE)isconstructedbyusingthetwoschemesattwoadjacentpoints.Weprovedthatthemethodisabsolutelystablebylinearizationanalysismethods.Onthebasisofthe(AGE)methodanalternatingsegmentimplicitmethodisconst

4、ructedwhicheachsegmenthas2p(3)pp≥pointsweprovethestabilitybylinearizationmethods.Withthefractionalstepmethodsagreatdealofnumericalexperimentstheirresultsdemonstratethatourmethodshaveadvantagesofcalculationbriefnesshigher

5、precisionsuitablefparallelcomputing.Inthepaperweconsideralsoaninitialperiodicboundaryconditionofdispersiveequationwithdiffusion.Anewdifferenceschemeeightasymmetricschemesareproposedanalternatingsegmentdifferenceschemeisc

6、onstructed.Theschemeisabsolutelystablesuitablefparallelcomputing.Numericalresultsdemonstratethattheschemehashigherprecisiongoodapplicability.Keywds:twodimensionalBurgersequationsdispersiveequationwithdiffusionfractionals