应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2011年
4期
712-717
,共6页
收敛性%稳定性%Euler-Maclaurin方法%分段连续项
收斂性%穩定性%Euler-Maclaurin方法%分段連續項
수렴성%은정성%Euler-Maclaurin방법%분단련속항
Convergence%Stability%Euler-Maclaurin method%Piecewise constant arguments
本文讨论了向前型分段连续微分方程Euler-Maclaurin方法的收敛性和稳定性,给出了Euler-Maclaurin方法的稳定条件,证明了方法的收敛阶是2n+2,并且得到了数值解稳定区域包含解析解稳定区域的条件,最后给出了一些数值例子用以验证本文结论的正确性.
本文討論瞭嚮前型分段連續微分方程Euler-Maclaurin方法的收斂性和穩定性,給齣瞭Euler-Maclaurin方法的穩定條件,證明瞭方法的收斂階是2n+2,併且得到瞭數值解穩定區域包含解析解穩定區域的條件,最後給齣瞭一些數值例子用以驗證本文結論的正確性.
본문토론료향전형분단련속미분방정Euler-Maclaurin방법적수렴성화은정성,급출료Euler-Maclaurin방법적은정조건,증명료방법적수렴계시2n+2,병차득도료수치해은정구역포함해석해은정구역적조건,최후급출료일사수치례자용이험증본문결론적정학성.
This paper is concerned with the convergence and the stability of Euler-Maclaurin methods for solutions of differential equations with piecewise constant arguments of advanced type.The conditions of stability for the Euler-Maclaurin methods are given.It is proved that the order of convergence is 2n + 2.And the conditions under which the numerical stability region contains the analytic stability region are obtained.Finally,several numerical examples are given to demonstrate our main results.
