数学分析论文new

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1、ARTICLEINPRESSComputersandMathematicswithApplications()ContentslistsavailableatScienceDirectComputersandMathematicswithApplicationsjournalhomepage:www.elsevier.com/locate/camwaApplicationofthevariationaliterationmethodtoinverseheatsourceproblemsFazhanGenga,b,,YingzhenLinaaDepartmentofMathematics,H

2、arbinInstituteofTechnology,Weihai,Shandong264209,ChinabDepartmentofMathematics,ChangshuInstituteofTechnology,Changshu,Jiangsu215500,ChinaarticleinfoabstractKeywords:ThispaperinvestigatestheinverseproblemofdeterminingaheatsourceintheparabolicInverseproblemheatequationusingtheusualconditions.Thenumeri

3、calsolutionisdevelopedbyusingtheUnknownsourcetermvariationaliterationmethod.ThismethodisbasedontheuseofLagrangemultipliersforHeatequationtheidentificationofoptimalvaluesofparametersinafunctional.UsingthismethodarapidVariationaliterationmethodconvergentsequencecanbeobtainedwhichtendstotheexactsolutio

4、noftheproblem.Furthermore,thevariationaliterationmethoddoesnotrequirethediscretizationoftheproblem.Thusthevariationaliterationmethodissuitableforfindingtheapproximationofthesolutionwithoutdiscretizationoftheproblem.Twonumericalexamplesarepresentedtoillustratethestrengthofthemethod.'2009ElsevierLtd.A

5、llrightsreserved.1.IntroductionIntheprocessoftransportation,diffusionandconductionofnaturalmaterials,thefollowingheatequationisinduced:2uta
uDf.x;tIu/;.x;t/2.0;T/;(1.1)whereurepresentsthestatevariable,aisthediffusioncoefficient,isaboundeddomaininRdandfdenotesphysicallaws,whichmeansasourcetermhere.

6、Therearemanyresearchesonsuchaninverseproblemofdeterminingthesourcetermfrom1970s,sincethecharacteristicofsourceinthepracticalproblemisalwaysunknown.However,thesolutionofthisproblemisunstable,hencetheinverseproblemisill-posed.Themajordifficultyinestablishinganynumericalalgorithmforapproximatingthesolu

7、tionistheill-posednessoftheproblemandtheill-conditioningoftheresultantdiscretizedmatrix.Theinverseproblemofdetermininganunknownheatsourcefunctionintheheatconductionequationhasbeenconsideredinmanypaper