泛函微分与泛函方程Runge-Kutta方法的稳定性分析
摘要
获得泛函微分与泛函方程Runge-Kutta方法关于非约束网格的稳定性结果.
基金
国家自然科学基金(批准号:19871070)
中国博士后科学基金
中国科学院王宽诚博士后工作奖励基金
参考文献7
-
1储钟武,邱深山,刘明珠.Convergence of a New Adapting Runge-Kutta Method to Delay Differential Equations[J].Journal of Harbin Institute of Technology(New Series),1996,3(4):1-4. 被引量:1
-
2张诚坚,周叔子.The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations[J].Science China Mathematics,1998,41(11):1151-1157. 被引量:16
-
3吴新元,李继春.关于数值求解常微分方程的二阶导数方法的最高可达阶及其Stiff稳定性[J].应用数学与计算数学学报,1990,4(1):35-44. 被引量:2
-
4Hong-jiong Tian,Jiao-xun Kuang,Lin Qiu.THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS[J].Journal of Computational Mathematics,2001,19(2):125-130. 被引量:4
-
5李宏智,李建国.求解延迟微分代数方程的多步Runge-Kutta方法的渐近稳定性[J].数学研究,2004,37(3):279-285. 被引量:6
-
6丛玉豪,杨彪,匡蛟勋.广义中立型系统的渐近稳定性及数值分析[J].计算数学,2001,23(4):457-468. 被引量:2
-
7余越昕,文立平.非线性中立型延迟积分微分方程单支方法的稳定性分析[J].应用数学,2009,22(2):291-296. 被引量:1
二级参考文献63
-
1田红炯,匡蛟勋.THE STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS[J].Numerical Mathematics A Journal of Chinese Universities(English Series),1995,4(1):10-16. 被引量:2
-
2王晚生,李寿佛.非线性中立型延迟微分方程稳定性分析[J].计算数学,2004,26(3):303-314. 被引量:18
-
3余越昕,李寿佛.非线性中立型延迟微分方程单支方法的数值稳定性[J].计算数学,2006,28(4):357-364. 被引量:8
-
4Zhu W J,Petzold L R.Asymptotic stability of linear delay differential-algebraic equations and numerical methods.Appl.Number.Math.,1997,24:247-264.
-
5Liu Y K.Runge-Kutta-collocation methods for systems of functional-differential and functional equations.Adv.Comput.Math.,1999,11:315-329.
-
6Ascher U M,Petzold L R.The numerical solution of delay-differential-algebraic equations of retarded and neutral type.SIAM J.Numer.Anal.,1995,32:1635-1657.
-
7Baker C T H,Paul C A H,Tian H.Differential algebraic equations with after-effect.J.Comput.Appl.Math.,2002,140:63-80.
-
8Brenan K E,Campbell S L,Petzold L R.Numerical solution of initial-value problems in differential-algebraic equations.North-Holland: Elsevier,1989.
-
9Li S F.B-convergence properties of multistep Runge-Kutta methods.math.Comput.,1994,62:565-575.
-
10In′t Hout K J.Stability analysis of Runge-Kutta methods for systems of delay differential equations.IMAJ.Numer.Anal.,1997,17:17-27.
共引文献25
-
1黄枝姣.单支方法关于多延迟Pantograph方程的稳定性分析[J].应用数学,2001,14(S1):217-220.
-
2CONG,Yu-hao(丛玉豪).NGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2001,22(7):827-835. 被引量:1
-
3余越昕,李寿佛.非线性中立型延迟微分方程Runge-Kutta方法的稳定性[J].系统仿真学报,2005,17(1):49-52. 被引量:6
-
4Si-qingGan,Wei-minZheng.STABILITY OF GENERAL LINEAR METHODS FOR SYSTEMS OF FUNCTIONAL-DIFFERENTIAL AND FUNCTIONAL EQUATIONS[J].Journal of Computational Mathematics,2005,23(1):37-48.
-
5余越昕,文立平.非线性中立型延迟微分方程单支θ-方法的稳定性[J].湘潭大学自然科学学报,2005,27(4):1-4. 被引量:1
-
6王雷,吴新元.一类k步2k+1阶刚性稳定的二阶导数方法[J].南京大学学报(数学半年刊),2006,23(1):149-156. 被引量:1
-
7余越昕,文立平,李寿佛.非线性中立型延迟微分方程线性Θ—方法的渐近稳定性[J].高等学校计算数学学报,2006,28(2):103-110. 被引量:4
-
8余越昕,李寿佛.非线性中立型延迟微分方程单支方法的数值稳定性[J].计算数学,2006,28(4):357-364. 被引量:8
-
9李超群.中立型延迟微分方程一般线性方法的非线性稳定性[J].应用数学学报,2008,31(2):249-256.
-
10王晚生,余越昕,李寿佛.一类线性多步法关于变延迟非线性中立型微分方程的渐近稳定性[J].高等学校计算数学学报,2008,30(2):169-177.