简介:Inthispaper,severalusuallyusedpolynomialinterpolationmethodsareexplainedinviewofvectorbasisanddimensioninlinearalgebratheory.Usingtransitionmatrixes,generalconversionformulabetweenthebasisfunctionsetsofthesepolynomialinterpolationmethodsaregiven.Anexamplealsoshowstheeffectivenessoftheresults.
简介:Inthispaper,weconsidertheCauchyproblemfortheLaplaceequation,whichisseverelyill-posedinthesensethatthesolutiondoesnotdependcontinuouslyonthedata.AmodifiedTikhonovregularizationmethodisproposedtosolvethisproblem.Anerrorestimatefortheaprioriparameterchoicebetweentheexactsolutionanditsregularizedapproximationisobtained.Moreover,anaposterioriparameterchoiceruleisproposedandastableerrorestimateisalsoobtained.Numericalexamplesillustratethevalidityandeffectivenessofthismethod.
简介:Basedonsomerecentresultsforinterlacingeigenvalueintervalsfrom1-parameterfamiliesofsequencesofeigenvalueinequalities,anewmethodisgiventosolvingtheindexproblemforSturm-Liouvilleeigenvaluesforcoupledself-adjointboundaryconditionsintheregularcase.ThekeyisanewcharacteristicprincipleforindicesforSturm-Liouvilleeigenvalues.Thealgorithmcorrespondingonthecharacteristicprinciplearediscussed,andnumericalexamplesarepresentedtoillustratethetheoreticalresultsandshowthatthealgorithmisvalid.
简介:Thealternatingdirectionmethodofmultipliers(ADMMforshort)isefficientforlinearlyconstrainedconvexoptimizationproblem.ThepracticalcomputationalcostofADMMdependsonthesub-problemsolvers.Theproximalpointalgorithmisacommonsub-problem-solver.However,theproximalparameterissensitiveintheproximalADMM.Inthispaper,weproposeahomotopy-basedproximallinearizedADMM,inwhichahomotopymethodisusedtosolvethesub-problemsateachiteration.Undersomesuitableconditions,theglobalconvergenceandtheconvergencerateofO(1/k)intheworstcaseoftheproposedmethodareproven.Somepreliminarynumericalresultsindicatethevalidityoftheproposedmethod.
简介:
简介:Basedonanimprovedfractionalsub-equationmethodinvolvingJumarie'smodifiedRiemann-Liouvillederivative,weconstructanalyticalsolutionsofspace-timefractionalcompoundKdV-BurgersequationandcoupledBurgers'equations.Theseresultsnotonlyrevealthatthemethodisveryeffectiveandsimpleinstudyingsolutionstothefractionalpartialdifferentialequation,butalsoincludesomenewexactsolutions.
简介:Bythemethodofdynamicalsystem,weconstructtheexacttravellingwavesolutionsofanewHamiltonianamplitudeequationandtheOstrovskyequation.Basedonthismethod,thenewexacttravellingwavesolutionsofthenewHamiltonianamplitudeequationandtheOstrovskyequation,suchassolitarywavesolutions,kinkandanti-kinkwavesolutionsandperiodictravellingwavesolutions,areobtained,respectively.
简介:Akindofsecond-orderimplicitfractionalstepcharacteristicfinitedifferencemethodispresentedinthispaperforthenumericallysimulationcoupledsystemofenhanced(chemical)oilproductioninporousmedia.Sometechniques,suchasthecalculusofvariations,energyanalysismethod,commutativityoftheproductsofdifferenceoperators,decompositionofhigh-orderdifferenceoperatorsandthetheoryofaprioriestimatesareintroducedandanoptimalordererrorestimatesinl~2normisderived.Thismethodhasbeenappliedsuccessfullytothenumericalsimulationofenhancedoilproductioninactualoilfields,andthesimulationresultsarequiteinterestingandsatisfactory.