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Numerical solution of nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel by spline quasi-interpolating projectors

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  • Aimi, A.
  • Leoni, M.A.
  • Remogna, S.

Abstract

Nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel are here taken into account and numerically solved by spline quasi-interpolating projectors based collocation and Kulkarni methods, both in their basic and iterated versions. Theoretical analysis of discretization error and convergence order is provided, together with numerical results validating the estimates obtained under the hypothesis of sufficiently smooth solutions. Finally, some results in case of less regular solutions show the robustness of the proposed approach even in a non smooth framework.

Suggested Citation

  • Aimi, A. & Leoni, M.A. & Remogna, S., 2024. "Numerical solution of nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel by spline quasi-interpolating projectors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 183-194.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:183-194
    DOI: 10.1016/j.matcom.2024.04.008
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    References listed on IDEAS

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    1. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Allouch, C. & Sablonnière, P. & Sbibih, D., 2011. "A modified Kulkarni's method based on a discrete spline quasi-interpolant," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1991-2000.
    3. Allouch, C. & Remogna, S. & Sbibih, D. & Tahrichi, M., 2021. "Superconvergent methods based on quasi-interpolating operators for fredholm integral equations of the second kind," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    4. Allouch, C. & Sbibih, D. & Tahrichi, M., 2018. "Numerical solutions of weakly singular Hammerstein integral equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 118-128.
    5. Aimi, A. & Diligenti, M. & Sampoli, M.L. & Sestini, A., 2016. "Isogemetric analysis and symmetric Galerkin BEM: A 2D numerical study," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 173-186.
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