鐵磁鏈方程的數(shù)值方法.pdf

1、青島海洋大學(xué)碩士學(xué)位論文鐵磁鏈方程的數(shù)值方法姓名：薛恒申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：謝樹(shù)森2002.6.1NumericalMethodsforFerromagneticEquationsAbstractUndertheconditionofzerodamping，theLandauLifchitzferromagneticequationscanbeconsideredasanabsolutelyintegrableiso

2、latedsubsystemManyphyrsicistshavestudiedtheexistence，thewayofinversescatterandtheintercollisionofitssolutionSomemathematiciansdeductedsuchpropertiesofthesolutionastheexistence，theuniqueness，theestimateoflongperiodbehavio

3、r，theexistenceofattractor，andtheestimateofHausdorffdimensionIntheresearchofnumericalsolutionsoftheLandau—Lifchitzequations，somephysicistssimulatedthepropertiesofthesolutionswithdifierencemethod，butthetheoreticalanalysiso

4、fnumericalmethodwashardlydone鼢achasbeendoneisthatLuBainianandFangShaomeiposeddifferencescheme，F(xiàn)ourierspectralandpseudospectralschemesforthezerodampingferromagneticequationandthat、ⅣanGuihuaposedanexplicitfinitedifferences

5、chemefortheequationwithGilbertdampingitemsThispaperiscomposedoftwoparts：Inthefirstchapter，alinearizedimplicitfinitedifferenceschemeisgiven，whichovercomestherestrictoftimestepofexplicitschemeConvergenceandstabilityofthesc

6、hemeisproved，andthe2orderconvergenceprecisionoftimeandspaceisobtainedInthesecondchapter，finiteelementmethodisusedtosolvetheferromagneticequationsEssentiallyLandauLifshitzequationsareaparabolicequationgroup，andtherearesom

7、eresearchresultsusedtosolvetheequationwithfiniteelementmethodWiththespecialpropertythatthecoefficientmatrixoftheequationgroupisdissymmetrythispapergeneralizestheresultsto3dimensionswhichsuitstheferromagneticequations，and

8、enrichesthenumericalmethodsofLandau—LifshitzequationsIntheendofeachchapter，thenumericalexperimentsareprovidedtocheckthetheoreticalresultskeywords：LandauLifshitzferromagneticequations，differencescheme，finiteelementmethod，