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<p>In this study, an efficient scheme is developed to solve a class of nonlinear third-kind Volterra integral equations through the four-block approach. The method is formulated based on the Gauss–Lobatto quadrature rule. Notably, the proposed method eliminates the need for starting values, enabling the simultaneous computation of four unknown function values within each block. The convergence of the scheme is thoroughly examined using Gronwall’s inequality. Finally, three nonlinear examples confirm the approach’s accuracy, robustness, and effectiveness.</p>

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A four-block scheme for nonlinear third-kind Volterra integral equations

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • F. Afiatdoust,
  • M. H. Heydari,
  • M. Bayram,
  • D. Baleanu

摘要

In this study, an efficient scheme is developed to solve a class of nonlinear third-kind Volterra integral equations through the four-block approach. The method is formulated based on the Gauss–Lobatto quadrature rule. Notably, the proposed method eliminates the need for starting values, enabling the simultaneous computation of four unknown function values within each block. The convergence of the scheme is thoroughly examined using Gronwall’s inequality. Finally, three nonlinear examples confirm the approach’s accuracy, robustness, and effectiveness.