30152.非線性多變延遲分微分方程rungekutta方法的穩(wěn)定性分析

1、非線性多變延遲積分微分方程RungeKutta方法的穩(wěn)定性分析專業(yè)名稱：應(yīng)用數(shù)學(xué)申請人：李旭旭指導(dǎo)教師：肖飛雁論文答辯委員會主席綽委員：紐幽委晁緇塹訟鳋f三絲邀選壘毯亟廣西師范大學(xué)碩士學(xué)位論文非線性多變延遲積分微分方程R1mg爭Kutta方法的穩(wěn)定性分析StabilityAnalysisofRungeKuttaMethodsforNonlinearMulti—VariableDelayIntegroDifferentialEquatio

2、nsAuthor：LiXuxuSupervisor：AProfXiaoFeiyanMajor：AppliedMathematicsSpeciality：NumericalMethodsofDifferentialEquationsGrade：2011ABSTRACTDelayintegrodiffcrentialequationsarisewidelyinthefieldsofphysics，biologymedicine，chemis

3、tryeconomics，ecologycontroltheoryandSOonConsideringthattheanalyticalsolutionsofdelayintegrodifferentialequationsaredifficulttobeobtained，theinvestigationofnumericalmethodsisverymeaningfulMoreover，stabilityisoneofbasilici

4、ndexestoweighthevalidityofamethodinnumericalanalysis，SOtheresearchofstabilityofnumericalmethodsisthemaintaskinnumericalanalysisThepresentpaperisdevotedtothestabilityanalysisofRungeKuttamethodsfornonlineardelayintegrodiff

5、erentialequations，andisorganizedasfollows：Inthefirstchapter，weintroduceapplicationbackgroundandresearchbackgroundofdelaydifferentialequations，andrecallthehistoryofitsstudyofanalyticalsolutionsandnumericalsolutionsThemain

6、innovationsofthisarticleareintroducedInthesecondchapter，weintroducetheresearchobjectofthisarticlequalitativeanalysisofnonlinearmultivariabledelayintegrodifferentialequationsInthethirdchapter，theRunge—Kuttamethodsareexten

7、dedandappliedtononlinearmultivariabledelayintegrodifferentialequations，somestabilityconditionsareabtainedInthefourthchapter，theERKmethodsaxeappliedtoseveralnonlineardelayintegrodifferentialequations，fromtheAngleofapplica

8、tion，verifythenumericalstabilityofthethirdchapter，thenumericaltestresultsshowthatthiscalculationmethodiSeffectiveinpracticalapplicationInthelast，thispapermadeasummaryprospectedthefutureresearchdirectionKeyWords：nonlinear