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Research Article

Numerical solution of nonlinear third-kind Volterra integral equations using an iterative collocation method

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Pages 2063-2076 | Received 02 Aug 2022, Accepted 28 Aug 2023, Published online: 25 Sep 2023

References

  • S.S. Allaei, Z.W. Yang, and H. Brunner, Existence, uniqueness and regularity of solutions to a class of third-kind Volterra integral equations, J. Integral Equ. Appl. 27 (2015), pp. 325–342.
  • M.A. Bartoshevich, On a heat conduction problem, Inz˘.-Fiz. Z˘. 2 (1975), pp. 340–346. (in Russian).
  • M.A. Bartoshevich, Expansion in one orthogonal system of Watson operators for solving heat conduction problems, Inz˘.-Fiz. Z˘. 3 (1975), pp. 516–522. (in Russian).
  • H. Brunner, Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge University Press, Cambridge, 2004.
  • H. Brunner, Volterra Integral Equations: An Introduction to Theory and Applications, Cambridge University Press, Cambridge, 2017.
  • P. Grandits, A regularity theorem for a Volterra equation of the third kind, J. Integral Equ. Appl. 4 (2008), pp. 1–21.
  • K. Kherchouche, A. Bellour, and P. Lima, Iterative collocation method for solving a class of nonlinear weakly singular Volterra integral equations, Dolomites Res. Notes Approx 14 (2021), pp. 33–41.
  • H. Laib, A. Bellour, and A. Boulmerka, Taylor collocation method for a system of nonlinear Volterra delay integro-differential equations with application to COVID-19 epidemic, Int. J. Comput. 99 (2022), pp. 852–876.
  • H. Laib, A. Boulmerka, A. Bellour, and F. Birem, Numerical solution of two-dimensional linear and nonlinear Volterra integral equations using Taylor collocation method, J. Comput. Appl. Math. 417 (2023), pp. 1–21.
  • M.J. Lighthill, Contributions to the theory of heat transfer through a laminar boundary layer, Proc. R. Soc. Lond. Ser. A. 202 (1950), pp. 359–377.
  • X. Ma and C. Huang, Recovery of high order accuracy in spectral collocation method for linear Volterra integral equations of the third-kind with non-smooth solutions, J. Comput. Appl. Math. 392 (2021), pp. 113458.
  • S. Nemati, P. Lima, and D. Torres, Numerical solution of a class of third-kind Volterra integral equations using Jacobi wavelets, Numer. Algorithms 86 (2021), pp. 675–691.
  • S. Nemati and P. Lima, Numerical solution of a third-kind Volterra integral equation using an operational matrix technique, in 2018, European Control Conference (ECC), Limassol. (2018), pp. 3215–3220.
  • K. Rouibah, A. Bellour, P. Lima, and E. Rawashdeh, Iterative continuous collocation method for solving nonlinear volterra integral equations, Kragujev. J. Math. 46 (2022), pp. 635–648.
  • Y. Rostami, A new wavelet method for solving a class of nonlinear partial integro-differential equations with weakly singular kernels, Math. Sci. 16 (2022), pp. 225–235.
  • Y. Rostami, An effective computational approach based on hermite wavelet Galerkin for solving parabolic Volterra partial integro differential equations and its convergence analysis, Math. Model. Anal. 28 (2023), pp. 163–179.
  • Y. Rostami, Two approximated techniques for solving of system of two-dimensional partial integral differential equations with weakly singular kernels, Comput. Appl. Math. 40 (2021), pp. 1–31.
  • Y. Rostami, Operational matrix of two dimensional Chebyshev wavelets and its applications in solving nonlinear partial integro-differential equations, Eng. Comput. 38 (2020), pp. 745–761.
  • Y. Rostami and K. Maleknejad, Comparison of two hybrid functions for numerical solution of nonlinear mixed partial integro-differential equations, Iran. J. Sci. Technol. Trans. Sci. 46 (2022), pp. 645–658.
  • Y. Rostami and K. Maleknejad, The solution of the nonlinear mixed partial integro-differential equation via two-dimensional hybrid functions, Mediterr. J. Math. 19 (2022), pp. 1–20.
  • H. Song, Y. Xiao, and M. Chen, Collocation methods for third-kind Volterra integral equations with proportional delays, Appl. Math. Comput. 388 (2020), pp. 1–11.
  • H. Song, Z. Yang, and H. Brunner, Analysis of collocation methods for nonlinear Volterra integral equations of the third kind, Calcolo 56 (2019), pp. 1–29.
  • G. Vainikko, Cordial Volterra integral equations 1, Numer. Funct. Anal. Optim. 30 (2009), pp. 1145–1172.
  • G. Vainikko, Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations, Numer. Funct. Anal. Optim. 32 (2011), pp. 83–109.
  • Z. Wang, M. Zhou, and Y. Guo, An hp-version Jacobi spectral collocation method for the third-kind VIEs, J. Sci. Comput. 87 (2021), pp. 1–15.

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