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1、Æ“Ò10530ÆÒ201510111129©aÒO241.81—?úma¬ÆØ©Banach˜m¥óÀò´‡©•§wª†éÛªRunge-Kutta•{•½5©ÛÆž<ùŒâ•P“{lÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••f5‡©•§êŠ•{"˜lco›FBanach˜m¥óÀò´‡©•§wª†éÛªRunge-Kutta•{•½5©ÛÆž<ùŒâ•P“{lÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••f5‡©•§êŠ•{Æž?OnÆa¬Æǃü‰ ŒÆØ©J
2、FÏ2018-04-10StabilityAnalysisofexplicitanddiagonalimplicitRunge-KuttaMethodsforImpulsiveDelayDi erentialEquationsinBanachSpaceCandidateDacaiLiangSupervisorandRankProfessorYuexinYuCollegeMathematicsandComputationalScienceProgramMathematicsSpecializationNu
3、mericalMethodsforSti Di erentialEquationsDegreeMasterofScienceUniversityXiangtanUniversityDateApril10th,2018IÁ‡Nõ¢S¯K¥,XÚG¬3,žm:u)]ma,¡•óÀy–.,˜•¡,XÚcG¬ÉLGK•,¡•ò´y–.éuùü«y–•XÚ,ÙêÆ .˜„•óÀò´‡©•§.Ïd§ïÄóÀò´‡©•§ƒ'nØw¿Â•Œ.éuóÀò´‡©•§½5nØïÄ®k¯õ¤J,Ù
4、ꊕ{ïÄâffm©,¤JØõ,…̇é‚5¯K½SȘm¥š‚5¯K.•d, ©3•˜„Banach˜m¥ïÄRunge-Kutta•{ꊕ½5,¼±ė(J:(1)ïÄBanach˜m¥˜aóÀò´‡©•§nØ)•½5,¿¼Ù•½5(J.(2)¼¦)þã¯Kawª†éÛªRunge-Kutta•{•½5(J,¿^ꊢy¤¼(J(5.'…cµóÀò´‡©•§;Runge-Kutta•{;Banach˜m;•½5;ìC•½5.IIAbstractInmanyprac
5、ticalproblems,thestateofthesystemwillinstantaneouslyjumpatcertainpointsintime,calledthepulsephenomenon.Ontheotherhand,thecurrentstateofthesystemwillbea ectedbythepaststate,knownasthedelayphenomenon.Thesystemthatco-existsbetweenthesetwophenom-ena,themathem
6、aticalmodelisgenerallyimpulsivedelaydi erentialequations.Therefore,itisgreatsigni cancetostudytherelatedtheoryoftheimpulsivedelaydi erentialequations.Therehavebeenmanyachievementsinthestudyofthequalitativetheoryofimpulsivedelaydi erentialequations,butthes
7、tudyofnumericalmethodshasonlyjustbegun.TheresultsarefewandmainlyaimatlinearproblemsornonlinearproblemsinHilbertspace.Forthisreason,thispaperstudiesthenumericalstabilityoftheRunge-KuttamethodinamoregeneralBanachspaceandobtainsthefollowingmainresults.(1)The
8、stabilityofthetheoreticalsolutionofaclassofimpulsivedelaydi erentialequationsinBanachspacesisstudiedandthestabilityresultsareobtained.(2)ThestabilityresultsoftheexplicitanddiagonalimplicitRunge-Kuttamethodsforsolvin
