简介：ConsiderabackwardheatequationinaboundeddomainΩR2withthenoisydataintheinitialtimegeometry.Theaimistofindthetemperaturefor0＜ε＜t＜T.Forthisill-posedproblem,theauthorsgiveacontinuousdependenceestimateofthesolution.Moreover,theconvergencerateoftheapproximatesolutionisalsogiven.

简介：一个方法为转换被描述在Laguerre多项式使用扩大并且把Mellin变换变换成Laplace变换的Mellin变换，然后，Laplace变换被合适的替换变换成第一个客气的卷绕旋转积分方程。那么获得的不可分的方程是一个提出病的问题，我们使用花键规则化解决它。方法的性能被在文学可得到的测试函数的倒置说明[J。Inst。数学。与Appl。20(1977)，p。73]，[J。数学。Comp。53(1989)，p。589]，[J。Sci。Stat。Comp。4(1983)，p。164]。方法的有效性被获得的结果显示出借助于桌子和图示威了。

简介：AnewmethodforapproximatingtheinerseLaplacetransformispresented.WefirstchangeourLaplacetransformequationintoaconvolutiontypeintegralequation,whereTikhonovregularizationtechniquesandtheFouriertransformationareeasilyapplied.WefinallyobtainaregularizedapproximationtotheinverseLaplacetransformasfinitesum

简介：Inthispaper,weconsideraninversescatteringproblemforanobstacleDR^2withRobinboundarycondition.Byapplyingthepointsource,wegivearegularizingmethodtorecoverthescatteredfieldfromthefar-fieldpattern.Numericalimplementationsarealsopresented.

简介：Regularizationmethodisaneffectivemethodforsolvingill-posedequation.Inthispapertheunbiasedestimationformulaofunitweightstandarddeviationintheregularizationsolutionisderivedandtheformulaisverifiedwithnumericalcaseof1000sampledatabyuseofthetypicalill-posedequation,i.e.theFredholmintegrationequationofthefirstkind.

简介：

简介：Inthispaperweconsideranon-standardinverseheatconductionproblemfordeterminingsurfaceheatfluxfromaninteriorobservationwhichappearsinsomeappliedsubjects.Thisproblemisill-posedinthesensethatthesolution(ifitexists)doesnotdependcontinuouslyonthedata.AFouriermethodisappliedtoformulatearegularizedapproximationsolution,andsomesharperrorestimatesarealsogiven.