188
Views
6
CrossRef citations to date
0
Altmetric
General articles

Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel

Pages 1230-1253 | Received 24 Oct 2017, Accepted 14 Aug 2018, Published online: 05 Sep 2018

References

  • M. Ahues, A. Largillier, and B.V. Limaye, Spectral Computations for Bounded Operators, Chapman and Hall/CRC, New York, 2001.
  • S.S. Allaei, T. Diogo, and M. Rebelo, The Jacobi collocation method for a class of nonlinear Volterra integral equations with weakly singular kernel, J. Sci. Comput. 69(2) (2016), pp. 673–695. doi: 10.1007/s10915-016-0213-x
  • C. Allouch, D. Sbibih, and M. Tahrichi, Numerical solutions of weakly singular Hammerstein integral equations, Appl. Math. Comp. 329 (2018), pp. 118–128. doi: 10.1016/j.amc.2018.01.046
  • K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, 1997.
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin, 2006.
  • Y. Chen and T. Tang, Convergence analysis of the Jacobi-spectral collocation methods for Volterra integral equations with a weakly singular kernel, Math. Comput. 79(269) (2010), pp. 147–167. doi: 10.1090/S0025-5718-09-02269-8
  • P. Das, G. Nelakanti, and G. Long, Discrete Legendre spectral projection methods for Fredholm Hammerstein integral equations, J. Comp. Appl. Math. 278 (2015), pp. 293–305. doi: 10.1016/j.cam.2014.10.012
  • P. Das, M.M. Sahani, G. Nelakanti, and G. Long, Legendre spectral projection methods for Fredholm Hammerstein integral equations, J. Sci. Comput. 68 (2016), pp. 213–230. doi: 10.1007/s10915-015-0135-z
  • B. Guo, Spectral Methods and their Applications, World Scientific, Singapore, 1998.
  • C. HaoTao, A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels, Sci. China Math. 57(10) (2014), pp. 2163–2178. doi: 10.1007/s11425-014-4806-2
  • Q. Huang and H. Xie, Superconvergence of Galerkin solutions for Hammerstein equations, Int. J. Numer. Anal. Model. 6(4) (2009), pp. 696–710s.
  • Q. Huang and S. Zhang, Superconvergence of interpolated collocation solutions for Hammerstein equations, Numer. Methods Partial Differential Eq. 26(2) (2010), pp. 290–304.
  • H. Kaneko, R. D. Noren, and P. A. Padilla, Superconvergence of the iterated collocation methods for Hammerstein equations, J. Comput. Appl. Math. 80(2) (1997), pp. 335–349. doi: 10.1016/S0377-0427(97)00040-X
  • H. Kaneko, R. Noren, and Y. Xu, Regularity of the solution of Hammerstein equations with weakly singular kernel, Integr. Equat. Oper. Th. 13 (1990), pp. 660–670. doi: 10.1007/BF01732317
  • H. Kaneko and Y. Xu, Superconvergence of the iterated Galerkin methods for Hammerstein equations, SIAM J. Numer. Anal. 33(3) (1996), pp. 1048–1064. doi: 10.1137/0733051
  • S. Kumar, The numerical solution of Hammerstein equations by a method based on polynomial collocation, J. Aust. Math. Soc. Ser. B 31(3) (1990), pp. 319–329. doi: 10.1017/S0334270000006676
  • B.L. Panigrahi, G. Long, and G. Nelakanti, Legendre multi-projection methods for solving eigenvalue problems for a compact integral operator, J. Comput. Appl. Math. 239 (2013), pp. 135–151. doi: 10.1016/j.cam.2012.09.014
  • B.L. Panigrahi and G. Nelakanti, Superconvergence of Legendre projection methods for the eigenvalue problem of a compact integral operator, J. Comput. Appl. Math. 235 (2011), pp. 2380–2391. doi: 10.1016/j.cam.2010.10.038
  • B.L. Panigrahi and G. Nelakanti, Legendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problem, J. Appl. Math. Comput. 43 (2013), pp. 175–197. doi: 10.1007/s12190-013-0658-0
  • S. Sohrabi, H. Ranjbar, and M. Saei, Convergence analysis of the Jacobi-collocation method for nonlinear weakly singular Volterra integral equations, Appl. Math. Comput. 299 (2017), pp. 141–152.
  • G.M. Vainikko, A perturbed Galerkin method and the general theory of approximate methods for non-linear equations, USSR Comput. Math. Phys. 7(4) (1967), pp. 1–41. doi: 10.1016/0041-5553(67)90140-1

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.