分段連續(xù)型微分方程的Euler-Maclaurin方法的穩(wěn)定性.pdf

1、中文摘要中文摘要本文主要研究自變量分段連續(xù)型延遲微分方程的收斂性與數(shù)值穩(wěn)定性。這類(lèi)方程在物理、生物和控制中有著廣泛的應(yīng)用。因此，對(duì)其數(shù)值解的研究具有重要的理論價(jià)值和實(shí)際意義。對(duì)于超前型自變量分段連續(xù)型延遲微分方程，研究了Euler—Maclaurin方法的收斂階和穩(wěn)定性。證明了n級(jí)Euler—Maclaurin方法對(duì)于超前型自變量分段連續(xù)型延遲微分方程的收斂階為2佗2，并得到了數(shù)值解的穩(wěn)定區(qū)域包含解析解穩(wěn)定區(qū)域的條件。對(duì)于具有無(wú)界延遲的

2、自變量分段連續(xù)型延遲微分方程，研究了EulerMaclaurin方法的收斂階和穩(wěn)定性。證明了n級(jí)EulerMaclaurin方法對(duì)于具有無(wú)界延遲的自變量分段連續(xù)型延遲微分方程的收斂階為2n2，并證明了對(duì)于所有的EulerMaclaurin方法，數(shù)值解的穩(wěn)定區(qū)域包含解析解的穩(wěn)定區(qū)域。另外，在每一部分的理論證明之后，都給出了相應(yīng)的數(shù)值算例。這些數(shù)值算例驗(yàn)證了理論上推出的結(jié)果的正確性。關(guān)鍵詞：自變量分段連續(xù)型延遲微分方程；EulerMacla

3、urin方法；穩(wěn)定性；收斂性簟●黑龍江大學(xué)碩士學(xué)位論文AbstractIIIIIlUIIIIIIIIMHl＼2124941ThispapermainlydealswiththeconvergenceandthenumericalstabilityofdelaydifferentialequationswithpiecewisecontinuousargumentsThiskindofequationshasconsiderableapp

4、licationstophysics，biologysystemsandcontroltheoryTherefore，thestabilityanalysisofthenumericalsolutionsisofimportanttheoreticalandpracticalsignificanceTheconvergenceandstabilityoftheEulerMaclaurinmethodfortheadvanceddelay

5、differentialequationswithpiecewisecontinuousargumentsareinvestigatedItiSprovedthatthenthEulerMaclaurinmethodisof2n2orderTheconditionsthatthestabilityregionofthenumericalsolutionscontainsthestabilityregionoftheanalyticsol

6、utionsareobtainedTheconvergenceandstabilityofthenumericalsolutionsfortheunboundedretardeddelaydifferentialequationswithpiecewisecontinuousargumentsisdiscussedinthispaperItisprovedthatthenthEulerMaclaurinmethodisof2譬2orde

7、r，andforallEulerMaclaurinmethod，thestabilityregionofthenumericalmethodcontainsthestabilityregionoftheanalyticsolutionsMoreover，therelevantnumericalexamplesaregivenineverypartTheseexperimentsverifytheresultsobtainedinthet