International Journal of Nonlinear Analysis and Applications

Laguerre-Chebyshev Petrov-Galerkin method for solving integral equations

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq

Abstract

This project aims to solve the second kind of Volterra, Fredholm integrodifferential equations, and mixed integral equations (VIDE, FIDEs and MIEs respectively) will be solved using the Laguerre-Chebyshev Petrov-Galerkin method (PGM). By solving three cases to show how the recommended technique works in this study, we established the PGM to find the approximate solution for linear VIDEs, FIDEs, and MIEs.

Keywords

[1] J. Abd Allah and H. Ali, Approximate solution of linear Volterra integrodifferential equation by Touchard polynomials method, Wasit J. Sci. Med. 11(2) (2018) 29–41.
[2] M.A. Abdou, Integral equation of mixed type and integrals, J. Comp. Appl. Math. 138 (2002) 273–285.
[3] A. AL-Jubory and S. Salih, Normalization Bernstein basis for solving fractional fredholm-integro differential equation, Ibn Al-Haitham J. Pure Appl. Sci. (2018) 490–499.
[4] A. AL-Mamun, W. Tao and M. Asaduzzaman, Solution of Volterra’s integro-differential equations by using variational iteration method, Peer J. Prepr. 164 (2019) 1–9.
[5] H. Al-Humedi and A. Munaty, The spectral Petrov-Galerkin method for solving integral equation of the first kind, Turk. J. Comput. Math. 12(13) (2021) 7856–7865.
[6] H.O. Al-Humedi and Z. Jameel, Combining cubic B-spline Galerkin method with quadratic weight function for solving partial integro-differential equations, J. Al-Qadisiyah Comput. Sci. Meth. 12(1) (2020) 9–20.
[7] W.W. Bell, Special Functions For Scientists Engineers, Dover Publications, London, 1968.
[8] J. Biazar and F. Salehi, Chebyshev Galerkin method for integro-differential equations of the second kind, Iran. J. Numer. Anal. Optim. 6(1) (2016) 31–42.
[9] J. Boyd, Chebyshev and Fourier Spectral Methods, DOVER Publications, New York, USA, 2013.
[10] C. Canuto, A. Hussaini and T.A. Zang, Spectral Methods Fundamentals in Single Domain, Springer-Verlag, Berlin, 2006.
[11] Z. Chen and S. Yuesheng, The Petrov-Galerkin and iterated Petrov-Galerkin method second kind integral, SIAM J. Number. Anal. 35(1) (1998) 406–434.
[12] J. Mamadu and L. Njoseh, Numerical solutions of Volterra equations using Galerkin method with certain orthogonal polynomials, J. Appl. Math. Phys. 4 (2016) 376–382.
[13] D. Maturi and M. Simbawa, The modified decomposition method for solving Volterra Fredholm integral-differential equations, Int. J. Geom. 18 (2020) 84–89.
[14] J. Naseif, The Petrov-Galerkin method for solving linear mixed Volterra-Fredholm integral equation via Boubaker polynomials, Al-Mustansiriyah J. Sci. 27 (2016) 76–81.
[15] D. Rani and V. Mishra, Solution of Volterra integral and integro-differential equations using modified LaplaceAdomian decomposition method, J. Appl. Math. Statist. Inf. 15 (2019) 5–18.
[16] K. Shah and T. Singh, Solution of second kind Volterra integral and integro-dofferential equation by homotopy analysis method, Int. J. Fuzzy Math. Arch. 6(4) (2015) 49–59.
[17] A.M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Heidelberg and Springer, Peking and Berlin, 2011.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 3227-3237
  • Receive Date: 07 October 2021
  • Revise Date: 01 November 2021
  • Accept Date: 20 December 2021