Discrete Legendre spectral projection methods for Fredholm–Hammerstein integral equations

Atkinson, 1992, A survey of numerical methods for solving nonlinear integral equations, J. Integral Equations Appl., 4, 15, 10.1216/jiea/1181075664 Ben-Yu, 1998 Long, 2009, Polynomially based multi-projection methods for Fredholm integral equations of the second kind, Appl. Math. Comput., 215, 147 Shen, 2006 Tang, 2008, On spectral methods for Volterra type integral equations and the convergence analysis, J. Comput. Math., 26, 825 Wan, 2009, Legendre spectral Galerkin method for second-kind Volterra integral equations, Front. Math. China, 4, 181, 10.1007/s11464-009-0002-z Xie, 2012, Convergence analysis of spectral Galerkin methods for Volterra type integral equations, J. Sci. Comput., 53, 414, 10.1007/s10915-012-9577-8 Atkinson, 1987, The discrete Galerkin method for integral equations, Math. Comp., 48, 595, 10.1090/S0025-5718-1987-0878693-6 Atkinson, 1993, The discrete collocation method for nonlinear integral equations, IMA J. Numer. Anal., 13, 195, 10.1093/imanum/13.2.195 Chen, 2007, The discrete multi-projection method for Fredholm integral equations of the second kind, J. Integral Equations Appl., 19, 143, 10.1216/jiea/1182525212 Kaneko, 1996, Superconvergence of the iterated Galerkin methods for Hammerstein equations, SIAM J. Numer. Anal., 33, 1048, 10.1137/0733051 Kumar, 1987, A new collocation-type method for Hammerstein integral equations, Math. Comp., 48, 585, 10.1090/S0025-5718-1987-0878692-4 Kumar, 1987, Superconvergence of a collocation-type method for Hammerstein equations, IMA J. Numer. Anal., 7, 313, 10.1093/imanum/7.3.313 Kaneko, 1997, Superconvergence of the iterated collocation methods for Hammerstein equations, J. Comput. Appl. Math., 80, 335, 10.1016/S0377-0427(97)00040-X Das, 2014, Legendre spectral projection methods for Urysohn integral equations, J. Comput. Appl. Math., 263, 88, 10.1016/j.cam.2013.12.002 Sahani, 2011 Atkinson, 1988, The discrete Galerkin method for nonlinear integral equations, J. Integral Equations Appl., 1, 17, 10.1216/JIE-1988-1-1-17 Golberg, 1996, Improved convergence rates for some discrete Galerkin methods, J. Integral Equations Appl., 8, 307, 10.1216/jiea/1181075955 Golberg, 1997 Golberg, 1998, Optimal convergence rates for some discrete projection methods, Appl. Math. Comput., 96, 237 Kumar, 1988, A discrete collocation-type method for Hammerstein equations, SIAM J. Numer. Anal., 25, 328, 10.1137/0725023 Kaneko, 1990, Regularity of the solution of Hammerstein equations with weakly singular kernels, Integral Equations Operator Theory, 13, 660, 10.1007/BF01732317 Sloan, 1995, Polynomial interpolation and hyperinterpolation over general regions, J. Approx. Theory, 83, 238, 10.1006/jath.1995.1119 Canuto, 2006 Ahues, 2001, vol. 18 Vainikko, 1967, A perturbed Galerkin method and the general theory of approximate methods of nonlinear equations, USSR Comput. Math. Math. Phys., 7, 1, 10.1016/0041-5553(67)90140-1 Schumaker, 1981 Kulkarni, 2003, Iterated discrete polynomially based Galerkin methods, Appl. Math. Comput., 146, 153 Suhubi, 2003