简介：Inliterature,nonlineartravelingwavesinelasticcircularrodshaveonlybeenstudiedbasedonsinglepartialdifferentialequation(pde)models,andhereweconsidersuchaproblembyusingamoreaccuratecoupled-pdemodel.WederivetheHamiltonianfromthemodelequationsforthelongfinite-amplitudewaveapproximation,analyzehowthenumberofsingularpointsofthesystemchangeswiththeparameters,andstudythefeaturesofthesesingularpointsqualitatively.Variousphysicallyacceptablenonlineartravelingwavesarealsodiscussed,andcorrespondingexamplesaregiven.Inparticular,wefindthatcertainwaves,whichcannotbecourltedbythesingle-equationmodel,canarise.

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简介：在laminar的非线性的传送对流的效果三维的Oldroyd-B液体流动被探讨。热转移现象被考虑非线性的热放射和热产生/吸收探索。边界层假设被考虑管理流动分析的数学模型。一些合适的类似变量被介绍把部分微分方程转变成平常的微分系统。有射击方法的Runge-Kutta-Fehlberg第四顺序、第五顺序的技术被用来获得无尺寸的速度和温度的答案。液体速度和温度上的各种各样的物理参数的效果被阴谋并且检验。比较与准确并且homotopy不安答案被做为粘滞液体大小写，和一根优秀火柴被注意。墙的数字价值砍在墙的压力和热转移率被公布并且调查。在德卜拉数字的价值的改进在液体速度上显示出反向的行为。当非线性的传送对流参数增加时，结果证明温度和热边界层被减少。Nusselt数字的价值比处于线性放射状况的那些处于非线性的放射状况是更高的。

简介：Fortwo-dimensionnonlinearconvectiondiffusionequation,atwo-gridmethodofcharacteristicsfinite-elementsolutionwasconstructed.Inthismethodthenonlineariterationsisonlytoexecuteonthecoarsegridandthefine-gridsolutioncanbeobtainedinasinglelinearstep.Forthenonlinearconvection-dominateddiffusionequation,thismethodcannotonlystabilizethenumericaloscillationbutalsoacceleratetheconvergenceandimprovethecomputationalefficiency.Theerroranalysisdemonstratesifthemeshsizesbetweencoarse-gridandfine-gridsatisfythecertainrelationship,thetwo-gridsolutionandthecharacteristicsfinite-elementsolutionhavethesameorderofaccuracy.Thenumericalexampleconfirmsthatthetwo-gridmethodismoreefficientthanthatofcharacteristicsfinite-elementmethod.

简介：Aself-adaptiveprecisealgorithminthetimedomainwasemployedtosolve2-Dnonlinearcoupledheatandmoisturetransferproblems.Byexpandingvariablesatadiscretizedtimeinterval,thevariationsofvariablescanbedescribedmoreprecisely,andanonlinearcoupledinitialandboundaryvalueproblemwasconvertedintoaseriesofrecurrentlinearboundaryvalueproblemswhicharesolvedbyFEtechnique.Inthecomputation,noadditionalassumptionandthenonlineariterationarerequired,andacriterionforself-adaptivecomputationisproposedtomaintainsufficientcomputingaccuracyforthechangesizesoftimesteps.Inthenumericalcomparison,thevariationsofmaterialpropertieswithtemperature,moisturecontent,andbothtemperatureandmoisturecontentaretakenintoaccount,respectively.Satisfactoryresultshavebeenobtained,indicatingthattheproposedapproachiscapableofdealingwithcomplexnonlinearproblems.