简介:StabilizedorChebyshevexplicitmethodshavebeenwidelyusedinthepasttosolvestiffordinarydifferentialequations.MakinguseofspecialpropertiesofChebyshev-likepolynomials,thesemethodshavefavorablestabilitypropertiescomparedtostandardexplicitmethodswhileremainingexplicit.Anewclassofsuchmethods,calledROCK,introducedin[Numer.Math.,90,1-18,2001]hasrecentlybeenextendedtostiffstochasticdifferentialequationsunderthenameS-ROCK[C.R.Acad.Sci.Paris,345(10),2007andCommun.Math.Sci,6(4),2008].InthispaperwediscusstheextensionoftheS-ROCKmethodstosystemswithdiscretenoiseandproposeanewclassofmethodsforsuchproblems,theT-ROCKmethods.Onemotivationforsuchmethodsisthesimulationofmulti-scaleorstiffchemicalkineticsystemsandsuchsystemsarethefocusofthispaper,butournewmethodscouldpotentiallybeinterestingforotherstiffsystemswithdiscretenoise.TwoversionsoftheT-ROCKmethodsarediscussedandtheirstabilitybehaviorisanalyzedonatestproblem.ComparedtotheT-leapingmethod,asignificantspeed-upcanbeachievedforsomestiffkineticsystems.Thebehavioroftheproposedmethodsaretestedonseveralnumericalexperiments.
简介:在这篇论文,我们考虑椭圆形的问题为第二份订单混合了有限元素方法。在最低顺序Brezzi-Douglas-Marini元素的情况中(如果d=2)orBrezzi-Douglas-Duran-Fortin元素(如果d=3)在矩形的平行六面体上,我们证明由合并某些照规则,混合方法系统能作为一个简单、以房间为中心的有限差别方法被写。这导致答案一稀少,positivesemidefinite为未知的数量的线性系统。为一个斜张肌系数,为未知的数量的稀少模式是五个点模板如果d=2,和七如果d=3。为一个一般张肌系数,它是九个点模板,并且十九分别地。是的混合方法实现的应用对的有限差别非等温多相,多,在多孔的媒介的部件流动被介绍。
简介:Anewhigh-ordertime-steppingfiniteelementmethodbaseduponthehigh-ordernumericalintegrationformulaisformulatedforSobolevequations,whosecomputationsconsistofaniterationprocedurecoupledwithasystemoftwoellipticequations.Theoptimalandsuperconvergenceerrorestimatesforthisnewmethodarederivedbothinspaceandintime.Also,aclassofnewerrorestimatesofconvergenceandsuperconvergenceforthetime-continuousfiniteelementmethodisdemonstratedinwhichtherearenotimederivativesoftheexactsolutioninvolved,suchthattheseestimatescanbeboundedbythenormsoftheknowndata.Moreover,someusefula-posteriorierrorestimatorsaregivenonthebasisofthesuperconvergenceestimates.
简介:为非强迫的优化在方法上介绍研究。学习的假设;主要结果;在简化Armijo类型下面的方法的集中性质衬里搜索。
简介:Inthispaper,theapplicationofhomotopymethodstotheloadflowmulti-solutionproblemsofpowersystemsisintroduced.BythegeneralizedBernshteintheorem,thecombinatorialnumberC2n^misshowntobetheBKKboundofthenumberofisolatedsolutionsofthepolynomialsystemtransformedfromloadflowequationswithgenericallychosencoefficients.AsaresultofthegeneralBezoutnumber,thenumberofpathsbeingfollowedisreducedsignificantlyinthepracticalloadflowcomputation.Finally,thecompleteP-Vcuresareobtainedbytrackingtheloadflowwithhomotopymethods.
简介:Aclassofnonconformingfiniteelementsisconsideredinthispaper,whichiscontinuousonlyatthenodesofthequasi-uniformmesh.Weshowthatthereex-istsanessentialestimatewhichindicatestheequivalencerelation,independentofthemeshparameter,betweentheenergiesofthenonconformingdiscreteharmonicextensionsindifferentsubdomains.Theessentialestimateisofgreatimportanceintheanalysisofthenonoverlappingdomaindecompositionmethodsappliedtosecondorderpartialdifferentialequationsdiscretizedbynonconformingfiniteele-ments.
简介:切开的修改Hermitian和skew-Hermitian(MHSS)重复方法和preconditionedMHSS(PMHSS)重复方法分别地被介绍。在纸,根据MHSS重复方法,我们在场为与non-Hermitian和复杂对称的积极definite/semi-definite解决大稀少的连续Sylvester方程的一个PMHSS重复方法矩阵。在合适的条件下面,我们证明PMHSS重复方法的集中并且讨论光谱preconditioned矩阵的性质。而且到计算花费了的还原剂,我们建立PMHSS重复方法的不精确的变体并且详细分析它的集中性质。数字结果证明PMHSS重复方法和它的不精确的变体是为连续Sylvester方程的这个类的有效、柔韧的解答者。
简介:1.IntroductionConsidertheboundaryvalueproblemofthePoissonequationwherefiisaconvexpolygonregon;r~OfftheboundaryofOandf(x,y)aknownfunctiononfi.Thegeneralizeddifferencemethodsonquadrilateralnetworksforellipticequationsareproposedin[11],’wheretheconverge...
简介:在这份报纸,我们在存在上解决一个问题结合线性多步方法(LMSM)的symplecticity,否定结果被获得。[从作者抽象]
简介:明确的问题在这篇论文被论述的为对称、积极的半的一般反复的方法上的集中分析。首先,提出了被精制为为反复的方法的精力标准集中的必要、足够的条件。为条件的一些解说性的例子也被提供。为明确的系统被获得仅仅依靠指导我们为一般连续潜水艇空间修正方法获得集中率身份的纯矩阵操作的为半的Gauss-Seidel方法的锋利的集中率身份。为连续潜水艇空间修正方法的集中率身份在本地修正计划拥有的新条件下面被获得本地精力标准集中。集中率估计然后以处于条件出现的准确潜水艇空格解答者和参数被导出。一致集中多,为一个模型问题的格子方法被集中率身份证明。工作能是regraded它为semidfinite问题的重复方法的集中上的统一并且简化的分析[8,9]。
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简介:可变的步尺寸的新多项式明确的表达线性multistep方法被介绍,在每个k步方法被k的一个固定集合描绘的地方-1或k参数。这构造包括最大的顺序的所有方法(p=k为生硬,并且p=k+1为nonstiff问题)。由建设支持时间步adaptivity,新明确的表达不基于扩大古典固定的步尺寸方法;相反古典的方法是在一个统一框架以内修理了步尺寸限制被获得。方法在Matlab被实现,与本地错误评价和大量步尺寸控制器。这为处于现实主义的运作的条件调查并且比较不同multistep方法提供一个平台。计算实验证明新multistep方法构造和实现有利地比作存在软件,尽管可变顺序还没被包括了。
简介:Inthisreview,weintendtoclarifytheunderlyingideasandtherelationsbetweenvariousmultigridmethodsrangingfromsubsetdecomposition,toprojectedsubspacedecompositionandtruncatedmultigrid.Inaddition,wepresentanovelgloballyconvergentinexactactivesetmethodwhichiscloselyrelatedtotruncatedmultigrid.Thenumericalpropertiesofalgorithmsarecarefullyassessedbymeansofadegenerateproblemandaproblemwithacomplicatedcoincidenceset.
简介:Inthispaper,weareconcernedwithuniformsuperconvergenceofGalerkinmethodsforsingularlyperturbedreaction-diffusionproblemsbyusingtwoShishkin-typemeshes.Basedonanestimateoftheerrorbetweensplineinterpolationoftheexactsolutionanditsnumericalapproximation,aninterpolationpost-processingtechniqueisappliedtotheoriginalnumericalsolution.Thisresultsinapproximationexhibitsuperconvergencewhichisuniformintheweightedenergynorm.Numericalexamplesarepresentedtodemonstratetheeffectivenessoftheinterpolationpost-processingtechniqueandtoverifythetheoreticalresultsobtainedinthispaper.
简介:Inthispaper,someeffectivecascadicmultigridmethodsareproposedforsolvingthelargescalesymmetricornonsymmetricalgebraicsystemsarisingfromthefinitevolumemethodsforsecondorderellipticproblems.Itisshownthatthesealgorithmsareoptimalinbothaccuracyandcomputationalcomplexity.Numericalexperimentsarereportedtosupportourtheory.