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On the convergence of multistep collocation methods for integral-algebraic equations of index 1

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Abstract

The multistep collocation method is introduced to solve integral-algebraic equations of index 1. The existence and uniqueness of the multistep collocation solution are proved. The convergence of the perturbed multistep collocation method is also investigated, which extends and includes the analysis of the multistep collocation method without perturbed terms. Some numerical experiments are given to illustrate the theoretical results.

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Authors and Affiliations

  1. Research Center of Satellite Technology, Harbin Institute of Technology, Harbin, 150080, People’s Republic of China

    Tingting Zhang & Shijie Zhang

  2. School of Science, Harbin Institute of Technology, Shenzhen, 518055, People’s Republic of China

    Hui Liang

Authors
  1. Tingting Zhang
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  2. Hui Liang
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  3. Shijie Zhang
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Correspondence to Shijie Zhang.

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Communicated by Antonio José Silva Neto.

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This work is supported by the National Nature Science Foundation of China (Nos. 11771128, 11101130), Fundamental Research Project of Shenzhen (JCYJ20190806143201649), Project (HIT.NSRIF.2020056) supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology, and Research Start-Up Fund Foundation in Harbin Institute of Technology (20190019).

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Zhang, T., Liang, H. & Zhang, S. On the convergence of multistep collocation methods for integral-algebraic equations of index 1. Comp. Appl. Math. 39, 294 (2020). https://doi.org/10.1007/s40314-020-01336-y

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  • DOI: https://doi.org/10.1007/s40314-020-01336-y

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