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Discontinuous piecewise polynomial collocation methods for integral-algebraic equations of Hessenberg type

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Abstract

This paper mainly focuses on the integral-algebraic equations (IAEs) of Hessenberg type. The tractability index is investigated. The existence, uniqueness, and regularity are analyzed, and the resolvent representation is given. First, the convergence theory of perturbed collocation methods in discontinuous piecewise polynomial space is established for first-kind Volterra integral equations, then it is used to derive the optimal convergence properties of discontinuous piecewise polynomial collocation methods for Hessenberg-type IAEs. Numerical examples illustrate the theoretical results.

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Authors and Affiliations

  1. School of Science, Harbin Institute of Technology, Shenzhen, 518055, China

    Hecong Gao & Hui Liang

Authors
  1. Hecong Gao
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  2. Hui Liang
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Correspondence to Hui Liang.

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Communicated by Cassio Oishi.

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The work was supported by the National Nature Science Foundation of China (Nos. 12171122, 11771128), Shenzhen Science and Technology Program (No. RCJC20210609103755110) and Fundamental Research Project of Shenzhen (No. JCYJ20190806143201649)

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Gao, H., Liang, H. Discontinuous piecewise polynomial collocation methods for integral-algebraic equations of Hessenberg type. Comp. Appl. Math. 41, 291 (2022). https://doi.org/10.1007/s40314-022-01998-w

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  • DOI: https://doi.org/10.1007/s40314-022-01998-w

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