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Convergence of one-leg methods for nonlinear neutral delay integro-differential equations

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Abstract

Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper.

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Authors and Affiliations

  1. School of Mathematics and Computational Sciences, Changsha University of Science and Technology, Changsha, 410004, China

    WanSheng Wang

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    ShouFu Li

Authors
  1. WanSheng Wang
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  2. ShouFu Li
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Corresponding author

Correspondence to WanSheng Wang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10871164), the Natural Science Foundation of Hunan Province (Grant No. 08JJ6002), and the Scientific Research Fund of Changsha University of Science and Technology (Grant No. 1004259)

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Wang, W., Li, S. Convergence of one-leg methods for nonlinear neutral delay integro-differential equations. Sci. China Ser. A-Math. 52, 1685–1698 (2009). https://doi.org/10.1007/s11425-009-0032-8

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  • DOI: https://doi.org/10.1007/s11425-009-0032-8

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