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An hp-version Spectral Collocation Method for Nonlinear Volterra Integro-differential Equation with Weakly Singular Kernels

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Abstract

In this paper, we present an hp-version Legendre–Jacobi spectral collocation method for the nonlinear Volterra integro-differential equations with weakly singular kernels. We derive hp-version error bounds of the collocation method under the \(H^1\)-norm for the Volterra integro-differential equations with smooth solutions on arbitrary meshes and singular solutions on quasi-uniform meshes. Numerical experiments demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Chuan-Li Wang

  2. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Zhong-Qing Wang

  3. Department of Mathematics, Donghua University, Shanghai, 200063, China

    Hong-Li Jia

  4. School of Mathematics and Statistics, Henan University of Science and Technology, Luo Yang, 471023, China

    Chuan-Li Wang

Authors
  1. Chuan-Li Wang
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  2. Zhong-Qing Wang
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  3. Hong-Li Jia
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Correspondence to Zhong-Qing Wang.

Additional information

The work is supported in part by the National Natural Science Foundation of China (Nos. 11571238, 11501098) and the Research Fund for Doctoral Program of Higher Education of China (No. 20133127110006).

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Wang, CL., Wang, ZQ. & Jia, HL. An hp-version Spectral Collocation Method for Nonlinear Volterra Integro-differential Equation with Weakly Singular Kernels. J Sci Comput 72, 647–678 (2017). https://doi.org/10.1007/s10915-017-0373-3

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  • DOI: https://doi.org/10.1007/s10915-017-0373-3

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