Modified Legendre rational and exponential collocation methods for solving nonlinear Hammerstein integral equations on the semi-infinite domain

References

• P.M. Anselone and J.W. Lee, Nonlinear integral equations on the half line, J. Integral Equ. Appl. 4(1) (1992), pp. 1–14.
   Google Scholar
• P.M. Anselone and I.H. Sloan, Integral equations on the half line, J. Integral Equ. Appl. 9(1) (1985), pp. 3–23.
   Google Scholar
• P.M. Anselone and I.H. Sloan, Numerical solutions of integral equations on the half line, Numer. Math. 51 (1987), pp. 599–614.
   Web of Science ®Google Scholar
• I.Y. Aref'eva and I.V. Volovich, Cosmological daemon, J. High Energy Phys. 2011(8) (2011), pp. 1–29.
   Google Scholar
• P Assari, F Asadi-Mehregan, and M Dehghan, On the numerical solution of Fredholm integral equations utilizing the local radial basis function method, Int. J. Comput. Math. 96(7) (2019), pp. 1416–1443.
   Web of Science ®Google Scholar
• K Atkinson, The numerical solution of integral equations on the half-line, SIAM. J. Numer. Anal. 6(3) (1969), pp. 375–397.
   Web of Science ®Google Scholar
• K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 1997.
   Google Scholar
• I Aziz, New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets, J. Comput. Appl. Math. 239 (2013), pp. 333–345.
   Web of Science ®Google Scholar
• I Aziz and F Khan, A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations, J. Comput. Appl. Math. 272 (2014), pp. 70–80.
   Web of Science ®Google Scholar
• D Barrera, F.E. Mokhtari, M.J. Ibáñez, and D. Sbibih, Non-uniform quasi-interpolation for solving Hammerstein integral equations, Int. J. Comput. Math. 97(1–2) (2020), pp. 72–84.
   Web of Science ®Google Scholar
• H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 1st ed., Springer-Verlag, New York, 2011.
   Google Scholar
• C. Canuto, M.Y. Hussaini, T.A. Zang, and A Quarteroni, Spectral Methods, 1st ed., Springer-Verlag, Berlin, Heidelberg, 2006.
   Google Scholar
• S. Chandrasekhar, Radiative Transfer, Dover Publications, Inc, New York, 1960.
   Google Scholar
• C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
   Google Scholar
• F. de Hoog and I.H. Sloan, The finite-section approximation for integral equations on the half-line, J. Aust. Math. Soc. Ser. B Appl. Math. 28(4) (1987), pp. 415–434.
   Google Scholar
• W.G. El-Sayed, Nonlinear functional integral equations of convolution type, Port. Math. 54 (1997), pp. 449–456.
   Google Scholar
• N.B. Engibaryan, On one problem of nonlinear radiation transfer, Astrofizika 2(1) (1966), pp. 31–36.
   Google Scholar
• M. Ganesh and M.C. Joshi, Numerical solutions of nonlinear integral equations on the half line, Numer. Funct. Anal. Optim. 10(11–12) (1989), pp. 1115–1138.
   Web of Science ®Google Scholar
• F. Hamani and A. Rahmoune, Solving nonlinear Volterra-Fredholm integral equations using an accurate spectral collocation method, Tatra Mt. Math. Publ. 80(3) (2021), pp. 35–52.
   Google Scholar
• H Hochstadt, Integral Equations, John Wiley, New York, 1973.
   Google Scholar
• A.K. Khachatryan and K.A. Khachatryan, Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear cases, Theor. Math. Phys. 172 (2012), pp. 1315–1320.
   Web of Science ®Google Scholar
• H. Khosravi, R. Allahyari, and A.S. Haghighi, Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on lp(R+), Appl. Math. Comput. 260 (2015), pp. 140–147.
   Web of Science ®Google Scholar
• R. Kress, Linear Integral Equations, 1st ed., Springer-Verlag, Berlin, Heidelberg, 1989.
   Google Scholar
• N.M.A.N. Long, Z.K. Eshkuratov, M. Yaghobifar, and M. Hasan, Numerical solution of infinite boundary integral equation by using Galerkin method with Laguerre polynomials, World Acad. Sci. Eng. Technol. Int. J. Math. Comput. Phys. Electr. Comput. Eng. 2 (2008), pp. 800–803.
   Google Scholar
• N. Madbouly, D. McGhee, and G. Roach, Adomian's method for Hammerstein integral equations arising from chemical reactor theory, Appl. Math. Comput. 117(2) (2001), pp. 241–249.
   Web of Science ®Google Scholar
• K. Maleknejad and A. Hoseingholipour, Numerical treatment of singular integral equation in unbounded domain, Int. J. Comput. Math. 98(8) (2021), pp. 1633–1647.
   Web of Science ®Google Scholar
• B.K. Mousavi, A.A. Hemmat, and F. Abdollahi, Wilson wavelets-based approximation method for solving nonlinear Fredholm-Hammerstein integral equations, Int. J. Comput. Math. 96(1) (2019), pp. 73–84.
   Web of Science ®Google Scholar
• N. Nahid, P. Das, and G. Nelakanti, Projection and multiprojection methods for nonlinear integral equations on the half-line, J. Comput. Appl. Math. 359 (2019), pp. 119–144.
   Web of Science ®Google Scholar
• N. Nahid and G.N. Nelakanti, Discrete projection methods for Hammerstein integral equations on the half-line, Calcolo 57(4) (2020), pp. 1–42.
   Web of Science ®Google Scholar
• N. Nahid and G. Nelakanti, Convergence analysis of Galerkin and multi-Galerkin methods for linear integral equations on half-line using Laguerre polynomials, Comput. Appl. Math. 38(182) (2019), p. 1.
   Google Scholar
• N. Nahid and G. Nelakanti, Convergence analysis of Galerkin and multi-Galerkin methods for nonlinear-Hammerstein integral equations on the half-line using Laguerre polynomials, Int. J. Comput. Math. 4(1) (2021), pp. 1–29.
   Web of Science ®Google Scholar
• A. Rahmoune, Spectral collocation method for solving Fredholm integral equations on the half-line, Appl. Math. Comput. 219(17) (2013), pp. 9254–9260.
   Web of Science ®Google Scholar
• A. Rahmoune, On the numerical solution of integral equations of the second kind over infinite intervals, J. Appl. Math. Comput. 66 (2021), pp. 129–148.
   Web of Science ®Google Scholar
• J. Shen and L. Wang, Some recent advances on spectral methods for unbounded domains, Commun. Comput. Phys. 5(2–4) (2009), pp. 195–241.
   Web of Science ®Google Scholar
• I.H. Sloan and A. Spence, Integral equations on the half-line: A modified finite-section approximation, Math. Comput. 47 (1986), pp. 589–595.
   Web of Science ®Google Scholar
• S. ul Islam, I. Aziz, and A. Al-Fhaid, An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders, J. Comput. Appl. Math. 260 (2014), pp. 449–469.
   Web of Science ®Google Scholar
• S. ul Islam, I. Aziz, and M. Fayyaz, A new approach for numerical solution of integro-differential equations via Haar wavelets, Int. J. Comput. Math. 90(9) (2013), pp. 1971–1989.
   Web of Science ®Google Scholar
• G. Vainikko, Galerkin's perturbation method and the general theory of approximate methods for non-linear equations, Ussr Comput. Math. Math. Phys. 7(4) (1967), pp. 1–41.
   Google Scholar
• V.S. Vladimirov, On the equation of the p-adic open string for the scalar tachyon field, Izv. Math. 69 (2005), pp. 487–512.
   Web of Science ®Google Scholar
• V.S. Vladimirov and Y.I. Volovich, Nonlinear dynamics equation in p-adic string theory, Theor. Math. Phys. 138 (2004), pp. 297–309.
   Web of Science ®Google Scholar