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Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations

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  • Wang, Wansheng
  • Li, Shoufu
  • Wang, Wenqiang

Abstract

In this paper, we show that under identical conditions which guarantee the contractivity of the theoretical solutions of general nonlinear NDDEs, the numerical solutions obtained by a class of linear multistep methods are also contractive.

Suggested Citation

  • Wang, Wansheng & Li, Shoufu & Wang, Wenqiang, 2009. "Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 421-425.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:421-425
    DOI: 10.1016/j.chaos.2007.07.080
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    References listed on IDEAS

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    1. Park, Ju H. & Kwon, O.M., 2008. "Stability analysis of certain nonlinear differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 450-453.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. Xiong, Wenjun & Liang, Jinling, 2007. "Novel stability criteria for neutral systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1735-1741.
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