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August 22, 2026International Journal of Computer Mathematics

A strategy for third-kind Hammerstein-type nonlinear Volterra integral equations

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Authors

PGP. GhorbanipourShiraz University of TechnologyMHM. H. HeydariShiraz University of TechnologyHDH. Laeli DastjerdiFarhangian University

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Overview

Numerical analysis demonstrates high-order convergence for third-kind Hammerstein Volterra integral equations via a discontinuous Galerkin scheme, confirming spectral accuracy.

Key Points

  • Develop and analyze a discontinuous Galerkin numerical scheme for third-kind Hammerstein-type nonlinear Volterra integral equations featuring time-dependent singularities.
  • Constructed a discontinuous Galerkin scheme on piecewise discontinuous polynomial spaces using shifted Legendre polynomials.
  • Proved solvability of the discrete system using a contractive fixed-point mapping under standard smoothness and Lipschitz continuity conditions.
  • Established rigorous error estimates proving high-order convergence, compactness, and stability of the numerical scheme.
  • Demonstrated spectral accuracy and verified theoretical convergence rates through numerical experiments.

Cite This Study

Ghorbanipour et al. (2026) studied this question.

synapsesocial.com/papers/6a895ec3ca7ade938187cefchttps://doi.org/10.1080/00207160.2026.2716757
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