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A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels

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  • Li Zhang
  • Jin Huang
  • Yubin Pan
  • Xiaoxia Wen

Abstract

In this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays. An improved Gronwall inequality is testified and adopted to prove the existence and uniqueness of the solution of the original equation. Then, we study the convergence and the error estimation of the mechanical quadrature method. Moreover, Richardson extrapolation based on the asymptotic expansion of error not only possesses a high accuracy but also has the posterior error estimate which can be used to design self-adaptive algorithm. Numerical experiments demonstrate the efficiency and applicability of the proposed method.

Suggested Citation

  • Li Zhang & Jin Huang & Yubin Pan & Xiaoxia Wen, 2019. "A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels," Complexity, Hindawi, vol. 2019, pages 1-12, June.
    • Handle: RePEc:hin:complx:4813802
    DOI: 10.1155/2019/4813802
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    References listed on IDEAS

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    1. Mosleh, Maryam & Otadi, Mahmood, 2015. "Least squares approximation method for the solution of Hammerstein–Volterra delay integral equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 105-110.
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