Contractivity and exponential stability of solutions to nonlinear neutral functional differential equations in banach spaces

详细信息    查看全文

• 作者：Wan-sheng Wang (1)
  Shou-fu Li (2)
  Run-sheng Yang (1)
  
• 关键词：nonlinear neutral functional differential equations ; contractivity ; exponential stability ; Banach spaces ; 34K40 ; 34K20
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：28
• 期：2
• 页码：289-304
• 全文大小：276KB
• 参考文献：1. Bellen, A., Zennaro, M. Strong contractivity properties of numerical methods for ordinary and delay differential equations. / Appl. Numer. Math., 9: 321鈥?46 (1992) CrossRef
  2. Bellen, A., Jackiewicz, Z., Zennaro, M. Contractivity of vaveform relaxation Runge-Kutta iterations and related limit methods for dissipative systems in the maximum norm. / SIAM J. Numer. Anal., 31: 499鈥?23 (1994) CrossRef
  3. Bellen, A., Zennaro, M. Numerical methods for delay differential equations. Oxford University Press, Oxford, 2003 CrossRef
  4. Bellen, A., Guglielmi, N., Zennaro, M. On the contractivity and asymptotic stability of systems of delay differential equations of neutral type. / BIT, 39: 1鈥?4 (1999) CrossRef
  5. Bellen, A., Guglielmi, N., Zennaro, M. Numerical stability of nonlinear delay differential equations of neutral type. / J. Comput. Appl. Math., 125: 251鈥?63 (2000) CrossRef
  6. Brunner, H., Vermiglio, R. Stability of solutions of delay functional integro-differential equations and their discretizations. / Computing, 71: 229鈥?45 (2003) CrossRef
  7. Gil鈥? M.I. Stability of finite and infinite dimensional systems. Kluwer Academic Publishers, Boston, 1998 CrossRef
  8. Hale, J. Theory of functional differential equations. Springer-Verlag, New York, 1977 CrossRef
  9. Huang, C.M., Fu, H.Y., Li, S.F., Chen, G.N. Stability analysis of Runge-Kutta methods for non-linear delay differential equations. / BIT, 39: 270鈥?80 (1999) CrossRef
  10. Huang, C.M., Li, S.F., Fu, H.Y., Chen, G.N. Nonlinear stability of general linear methods for delay differential equations. / BIT, 42: 380鈥?92 (2002) CrossRef
  11. Kolmanovskii, V.B., Myshkis, A. Introduction to the theory and applications of functional differential equations. Kluwer Academy, Dordrecht, 1999
  12. Kraaijevanger, J.F.B.M. Contractivity of Runge-Kutta methods. / BIT, 31: 482鈥?28 (1991) CrossRef
  13. Kuang, J.X., Cong, Y.H. Stability of numerical methods for delay differential equations. Science Press, Beijing, 2005
  14. Lancaster, P., Tismenetsky, M. The theory of matrices. Academic Press, Orlando, 1985
  15. Li, S.F. Nonlinear stability of a class of linear multistep methods. / Numer. Math. A J. of Chinese Univ., 9: 110鈥?18 (1987)
  16. Li, S.F. Theory of computational methods for stiff differential equations. Hunan Science and Technology Publisher, Changsha, 1997
  17. Li, S.F. Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces. / Sci. China (Series A), 35: 286鈥?01 (2005)
  18. Li, S.F. B-theory of Runge-Kutta methods for stiff Volterra functional differential equations. / Science in China (Series A), 46: 662鈥?74 (2003) CrossRef
  19. Li, S.F. B-theory of general linear methods for stiff Volterra functional differential equations. / Appl. Numer. Math., 53: 57鈥?2 (2005) CrossRef
  20. Li, S.F. High order contractive Runge-Kutta methods for Volterra functional differential equations. / SIAM J. Numer. Anal., 47: 4290鈥?325 (2010) CrossRef
  21. Li, S.L., Wen, L.Z. Functional differential equations. Hunan Science and Technology Publisher, Changsha, 1985
  22. Sand, J., Skelboe, S. Stability of backward Euler multirate methods and convergence of waveform relaxation. / BIT, 32: 350鈥?66 (1992) CrossRef
  23. Torelli, L. Stability of numerical methods for delay differential equations. / J. Comput. Appl. Math., 25: 15鈥?6 (1989) CrossRef
  24. Wang, W.S., Li, S.F. Stability analysis of nonlinear delay differential equations of neutral type. / Math. Num. Sinica, 26: 303鈥?14 (2004)
  25. Wang, W.S., Li, S.F. On the One-leg 螛-methods for solving nonlinear neutral functional differential equations. / Appl. Math. Comput., 193: 285鈥?01 (2007) CrossRef
  26. Wang, W.S., Zhang Y., Li, S.F. Nonlinear stability of one-leg methods for delay differential equations of neutal type. / Appl. Numer. Math., 58: 122鈥?30 (2008) CrossRef
  27. Wang, W.S., Li, S.F., Su, K. Nonlinear stability of Runge-Kutta methods for neutral delay differential equations. / J. Comput. Appl. Math., 214: 175鈥?85 (2008) CrossRef
  28. Wang, W.S., Li, S.F., Su, K. Nonlinear stability of general linear methods for neutral delay differential equations. / J. Comput. Appl. Math., 224: 592鈥?01 (2009) CrossRef
  29. Wang, W.S., Wen, L.P., Li, S.F. Nonlinear stability of 螛-methods for neutral differential equations in Banach space. / Appl. Math. Comput., 198: 742鈥?53 (2008) CrossRef
  30. Wen, L.P., Yu, Y.X., Li, S.F. The test problem class of Volterra functional differential equations in Banach space. / Appl. Math. Comput., 179: 30鈥?8 (2006) CrossRef
  31. Zennaro, M. Contractivity of Runge-Kutta methods with respect to forcing terms. / Appl. Numer. Math., 10: 321鈥?45 (1993) CrossRef
  32. Zennaro, M. Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations. / Numer. Math., 77: 549鈥?63 (1997) CrossRef
  33. Zhang, C.J., Li, S.F. Dissipativity and exponential asymptotic stability of the solutions for nonlinear neutral functional differential equations. / Appl. Math. Comput., 119: 109鈥?15 (2001) CrossRef
  34. Zhang, C.J. Nonlinear stability of natural Runge-Kutta methods for neutral delay differential equations. / J. Comput. Math., 20: 583鈥?90 (2002)
  35. Zhang, C.J., Vandewalle, S. Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization. / J. Comput. Appl. Math., 164鈥?65: 797鈥?14 (2004) CrossRef
  36. Zhang, C.J., Vandewalle, S. Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. / IMA J. Numer. Anal., 24: 193鈥?14 (2004) CrossRef
  37. Zhang, C.J., Vandewalle, S. General linear methods for Volterra integro-differential equations with memory. / SIAM J. Sci. Comput., 27: 2010鈥?031 (2006) CrossRef
  38. Zubik-kowal, B., Vandewalle, S. Waveform relaxation for functional-differential equations. / SIAM J. Sci. Comput., 21: 207鈥?26 (1999) CrossRef
  
• 作者单位：Wan-sheng Wang (1)
  Shou-fu Li (2)
  Run-sheng Yang (1)
  
  1. School of Mathematics and Computational Science, Changsha University of Science & Technology, Yuntang Campus, Changsha, 410114, China
  2. School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, 411105, China
  
• ISSN：1618-3932

文摘

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained, which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs), neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.