變分迭代法的若干研究.pdf

1、浙江大學理學院碩士學位論文變分迭代法的若干研究姓名：張宋宋申請學位級別：碩士專業(yè)：計算數學指導教師：韓丹夫20080601AbstractThispaperismainlyaboutsomeapplicationofVIMinthenumericalsolutionofintegralequationsTherearefourchaptersina11First，wemakeasimpleintroductionaboutthecomm

2、onmethodsoftheanmericalsolutiontointegralequations，includingiterativemethodsandprojectivemethodsAllthesemethodsmakeabasisofVIMAtthesametime，wegivetheknowledgeofvariation，whichisthetheorybasisofVIMInchapter2，wegiveaneleme

3、ntaryintroductiontotheconceptofVIMFirst，themainconceptsinVIM，suchasgeneralLagrangemultiplier，restrictedvariation，correctionfunctional，areexplainedheuristicallySubsequentlywegivetheprocedureofVIMandasimplestatementaboutth

4、econvergenceInchapter3，theVIMisappliedtosolvetheintegralequationssystemofthesecondkind，includingtheFredholmintegralequationssystemofthesecondkindandVolterraintegralequationssystemofthesecondkindWegivetheconcreteVIMforthe

5、integralequationssystemofthesecondkindThekeyliesinthederivationoftheequations，whichmakestheVIMfeasibleThen，wecangivetheiterativeformulawithoutdifficultyLast，twonumericalexamplesshowOurmethodisefficientandhavinganobviousa

6、dvantagecomparedwiththerelatedreferenceChapter4ismainlyabouttheapplicationofVIMinhigh—orderintegrodifferentialequations臃giveanindirectVIMtosolvehigh—orderVolterraintegrodifferentialequations，thatis，reducingthehigh—orderV

7、olterraintegrodifferentialequationstoanordinarysystemofequations，thenmakinganiterativeformulaforeachvariablesThismethodgivesasimpleexpressionofLagrangemultiplierA，ieA=1，whichsave8theproceduretocomputeALast，thenumericalre

8、sultsobtainedwithminimumamountofcomputationarecomparedwiththeexactsolutionsandtheresultsfromrelatedreferencetoshowtheefficiencyofthemethodTheresultsshowthatourmethodisofhighaccuracyandefficientforsolvinghigh—orderVolterr