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A computational approach for the non-smooth solution of non-linear weakly singular Volterra integral equation with proportional delay

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Abstract

This paper develops a well-conditioned Jacobi spectral Galerkin method for the analysis of Volterra-Hammerstein integral equations with weakly singular kernels and proportional delay. A recursive formula reduces the computational load when approximating the solutions of badly conditioned and complex non-linear algebraic systems. Additionally, the convergence properties of the method are also investigated. The spectral accuracy is obtained regardless of the discontinuities in the derivatives solution. Three examples illustrate the performance of the new approach.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

    P. Mokhtary

  2. Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    B. P. Moghaddam

  3. UISPA—LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    B. P. Moghaddam & A. M. Lopes

  4. Department of Electrical Engineering, Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

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  1. P. Mokhtary
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  2. B. P. Moghaddam
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  3. A. M. Lopes
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  4. J. A. Tenreiro Machado
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Correspondence to B. P. Moghaddam.

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Mokhtary, P., Moghaddam, B.P., Lopes, A.M. et al. A computational approach for the non-smooth solution of non-linear weakly singular Volterra integral equation with proportional delay. Numer Algor 83, 987–1006 (2020). https://doi.org/10.1007/s11075-019-00712-y

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  • DOI: https://doi.org/10.1007/s11075-019-00712-y

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