微分特征列法理論研究及應(yīng)用.pdf

1、大連理工大學(xué)博士學(xué)位論文微分特征列法理論研究及應(yīng)用姓名：陳玉福申請(qǐng)學(xué)位級(jí)別：博士專(zhuān)業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：張鴻慶1999.5.1AbstractInthispaperthetlleoryandapplicationaboutdifferentialcharacteristicsequencemethodwerediscussedwhichinvolvesthetheoriesofdi＆rentialequationsabstractalg

2、ebraandcomputeralgebraThebasicideaduetoJFRittandWuwentsunandtherelatedtheoryandalgorithmswereimprovedSomeprogramsfortheimportantalgorithms，suchasdeterminingthecharacteristicsequence，weregiveninMaplelanguage1Acomstructive

3、proofonthetheoremoffinitedifierentiaipolynomialbaseWasgivenThestructureofdi彘rentialpolinomiai’SzerosWasrefened111econceptofadjointidealwithareducedascendingchainofdiffcrentialpolynomialsWasfirstproposedanditsbasicpropert

4、ieswerediscussed，2Gavea1emnlaontheexistenceofpolynomialsin西yenvariants，whichsimplifiestheresultentthoryonalgebraicordifierentialpolynomials3Anewmethodtoudge“whetheranadjointidealofareducedascendascendingchainisornotaprim

5、eideal”WasgivenwhechiSeasiertobemanipultedthanothers4AunifiedtheoryoncompletionofafiniteindexsetWaSproposedinwhichauthorintruducedtheconceptofclosedsetandtheSOealledparti—tionprolongationalgfithrnfordeteminingtheclorueof

6、agivenfiIliteindexvectorsetTheseworksimplifysomecompletionalgorithmsknowntous5Accordingtotheprincipleofpartitionprolongationalgorithm，authorGaveanalgorithmtodetetminetheintegrableconditionsoncompleteortho—nomicsystem6For

7、1ineardifferentalequationsanewmethodfordeterminingthesizeofsolutionsWaSgiven，whichisanimprovementofSchwarz’Smethodfordeterminingthesizeofsymmetrygroups7Proposednormalfonnandthemethodtotransf01Tnagivendifierentialequation

8、stothenormalfornlGaveanalgorithmtodetermineTaylorexpansionsofanalyticsolutionsforthenormalform8Discussedthecompatibleeonditionsforakindofiineardifierentialequations，proposedanunifiedalgorithmforitKEYWORDSANDPHRASEScomput

9、eralgebra，alpgrithms，differentialpolynomials，characteristicsequences，completion，integrabilityconditions，differentialalgebraicmanifolds，primeideals，differentialequations，symmetrygroups，anal)ticsolutions，standardformsAMS(1