一类非线性脉冲延迟微分方程runge-kutta方法的稳定性分析

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1、Æ“è10530ÆÒ201510111166©aÒO241.81—?a¬ÆØ©˜aš‚5óÀò´‡©•§Runge-Kutta•{•½5©ÛÆž<±ï••P“{lÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••f5‡©•§êŠ•{"˜lco›F˜aš‚5óÀò´‡©•§Runge-Kutta•{•½5©ÛÆž<±ï•“6¶9…¡{lÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••f5‡©•§êŠ•{Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2018–4–10StabilityanalysisofRunge-Kuttamethodsforaclas

2、sofnonlinearimpulsivedelaydierentialequationsCandidateJianwenZhouSupervisorProfessorYuexinYuCollegeMathematicsandComputationalScienceProgramMathematicsSpecializationNumericalMethodsforStiDierentialEquationsDegreeMasterofScienceUniversityXiangtanUniversityDateApril10th,2018Á‡óÀò´‡©•§3gÄ››!)Ô

3、Æ!šÆ!zÆ!²LƯõ‰Æ†ó§+•k2•A^§Ùꊕ{ïÄäk•‡nØÚ¢S¿Â"duóÀÚž¢K•§¦Ta¯KïÄC›©E,Ú(J§ƒ'©zØõ§…̇8¥u‚5¯KÚAÏš‚5¯K"k•ud§©é˜aš‚5óÀò´‡©•§§Äk‰Ñ¯KnØ)•½5ÚìC•½5^‡§ÙgòRunge-Kutta•{^u¦)Ta¯K§(JL²§3˜½^‡e§“ꕽRunge-Kutta•{U±¯K•½†ìC•½5§•êŠÁ(Jy¤¼nØ(J(5"'…cµš‚5óÀò´‡©•§¶Runge-Kutta•{¶SȘm¶•½5¶ìC•½5"IAbs

4、tractImpulsivedelaydierentialequationsarewidelyusedinmanyfieldsofscienceandengineering,suchasautomaticcontrol,biology,medicine,chemistry,economicsandsoon.Itissignificanttostudythenumericalmethodsforimpulsivedelaydier-entialequations.Duetotheinfluenceofimpulseandtimedelay,theresearchofthiskindo

5、fproblemisverycomplicatedanddicult.Therelatedliteratureisnotmuch,andmainlyfocusonlinearproblemsandspecialnonlinearproblems.Inviewofthis,thepresentpaperdealswiththenumericalstabilityofRunge-Kuttamethodsforaclassofnonlinearimpulsivedelaydierentialequations.Firstly,thestabilityandasymptot-ics

6、tabilityconditionsforthetheoreticalsolutionoftheproblemaregiven.Secondly,theRunge-Kuttamethodsareappliedtosolvetheproblem.TheresultsshowthatthealgebraicallystableRunge-Kuttamethodscanpreservethestabilityandasymptoticstabilityundercertainconditions.Numericalexperimentsaregivetoconfirmthethe-o

7、reticalresultsintheend.KeywordsµNonlinearimpulsivedelaydierentialequations¶Runge-Kuttamethod-s¶Innerproductspace¶Stability¶Asymptoticstability.II8¹Á‡.......................................................................IAbstract.........................