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。這類方程在物理、生物和控制中有著廣泛的應用。因此，對其數(shù)值解的研究具有重要的理論價值和實際意義。對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Euler—Maclaurin方法對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。對于具有無界延遲的

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EulerMaclaurin方法對于具有無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，都給出了相應的數(shù)值算例。這些數(shù)值算例驗證了理論上推出的結(jié)果的正確性。關鍵詞：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●黑龍江大學碩士學位論文AbstractIIIIIlUIIIIIIIIMHl＼2124941ThispapermainlydealswiththeconvergenceandthenumericalstabilityofdelaydifferentialequationswithpiecewisecontinuousargumentsThiskindofequationshasconsiderableapp

4、licationstophysics，biologysystemsandcontroltheoryTherefore，thestabilityanalysisofthenumericalsolutionsisofimportanttheoreticalandpracticalsignificanceTheconvergenceandstabilityoftheEulerMaclaurinmethodfortheadvanceddelay

5、differentialequationswithpiecewisecontinuousargumentsareinvestigatedItiSprovedthatthenthEulerMaclaurinmethodisof2n2orderTheconditionsthatthestabilityregionofthenumericalsolutionscontainsthestabilityregionoftheanalyticsol

6、utionsareobtainedTheconvergenceandstabilityofthenumericalsolutionsfortheunboundedretardeddelaydifferentialequationswithpiecewisecontinuousargumentsisdiscussedinthispaperItisprovedthatthenthEulerMaclaurinmethodisof2譬2orde

7、r，andforallEulerMaclaurinmethod，thestabilityregionofthenumericalmethodcontainsthestabilityregionoftheanalyticsolutionsMoreover，therelevantnumericalexamplesaregivenineverypartTheseexperimentsverifytheresultsobtainedinthet