[1] M.A. Abdou, Khamis I. Mohamed, A.S. Ismail, On the numerical solutions of FredholmVolterra
integral equation, Applied mathematics and computation, 146(2-3) 2003, 713-728.
[2] H. Asgharzadeh, I. Borazjani, A NewtonKrylov method with an approximate analytical Jacobian
for implicit solution of NavierStokes equations on staggered overset-curvilinear grids with immersed
boundaries, Journal of computational physics, 331 2017, 227-256.
[3] J. Boersma and E. Danick, On the solution of an integral equation arising in potential problems for
circular and elliptic disks, SIAM Journal on Applied Mathematics, 53(4) 1993, 931-941.
[4] J.P. Boyd, Chebyshev and Fourier spectral methods, 2nd ed, New York Dover, 2000.
[5] R.L. Burden, J.D. Faires, Numerical Analysis, Youngstown State University, Youngstown, 2001.
[6] Y. Chen, C. Shen, A Jacobian-free Newton-GMRES (m) method with adaptive preconditioner and its
application for power
ow calculations, IEEE Transactions on Power Systems, 21(3) 2006, 1096-1103.
[7] J. Chen, C. Vuik, Globalization technique for projected NewtonKrylov methods, International Journal
for Numerical Methods in Engineering, 110(7) 2017, 661-674.
[8] D. Fadrani, V. Rostami, K. Maleknejad, Fast iterative methods for solving of boundary nonlinear
integral equations with singularity, Journal of Computational Analysis and Applications, 1(2) 1999,
219-234.
[9] D. Fadrani, V. Rostami, K. Maleknejad, Preconditioners for solving stochastic boundary integral
equations with weakly singular kernels, Computing, 63(1) 1999, 47-67.
[10] Z. Gouyandeh, T. Allahviranloo, A. Armand, Numerical solution of nonlinear VolterraFredholmHam-
merstein integral equations via Tau-collocation method with convergence analysis, Journal of Com-
putational and Applied Mathematics 100(308) 2016, 435-446.
[11] M. Hadizadeh, R. Azizi, A reliable computational approach for approximate solution of Hammerstein
integral equations of mixed type, International Journal of Computer Mathematics 81(7) 2004, 889-900.
[12] M. Hadizadeh, M. Mohamadsohi, Numerical solvability of a class of Volterra-Hammerstein integral
equations with noncompact kernels, Journal of Applied Mathematics, 2005(2) 2005, 171-181.
[13] S. Hatamzadeh-Varmazyar, M. Naser-Moghadasi, E. Babolian, Z. Masouri, Numerical approach to
survey the problem of electromagnetic scattering from resistive strips based on using a set of orthogonal
basis functions, Progress In Electromagnetics Research, 81 2008, 393-412.
[14] G. Han, Asymptotic error expansion variation of a collocation method for VolterraHammerstein equa-
tions, Appl. Numer. Math, 13 1993, 357-369.
[15] D.A. Knoll, D.E. Keyes, Jacobian-free Newton-Krylov methods: a survey of approaches and applica-
tions, Journal of Computational Physics, 193(2) 2004, 357-397.
[16] E.V. Kovalenko, Some approximate methods of solving integral equations of mixed problems, Journal
of Applied Mathematics and Mechanics, 53(1) 1989, 85-92.
[17] F. Li, Y. Li, Z. Liang, Existence of solutions to nonlinear Hammerstein integral equations and appli-
cations, Journal of Mathematical Analysis and Applications, 323(1) 2006, 209-227.
[18] M. Lakestani, M. Razzaghi, M. Dehghan, Solution of nonlinear Fredholm-Hammerstein integral equa-
tions by using semiorthogonal spline wavelets, Mathematical problems in engineering, 2005(1) 2005,
113-121.
[19] L.J. Lardy, A Variation of Nystrm's Method for Hammerstein Equations, The Journal of Integral
Equations, 1981, 43-60.
[20] A.V. Manzhirov, A mixed integral equation of mechanics and a generalized projection method of its
solution, Doklady Physics, 61(10) 2016.
[21] H.R. Marzban, H.R. Tabrizidooz, M. Razzaghi, A composite collocation method for the nonlinear
mixed VolterraFredholmHammerstein integral equations, Communications in Nonlinear Science and
Numerical Simulation, 16(3) 2011, 1186-1194.
[22] M.V. Mirkin and A.J. Bard, Multidimensional integral equations: a new approach to solving micro-
electrode diffusion problems: Part 2. Applications to microband electrodes and the scanning electro-
chemical microscope, Journal of Electroanalytical Chemistry, 323(1-2) 1992, 29-51.
[23] Y. Ordokhani, Solution of nonlinear VolterraFredholmHammerstein integral equations via rationalized
Haar functions, Applied Mathematics and Computation, 180(2) 2006, 436-443.
[24] Y. Ordokhani, Solution of FredholmHammerstein integral equations with WalshHybrid functions,
International Mathematical Forum, 4(20) 2009.
[25] K. Parand, A. Bahramnezhad, H. Farahani, A numerical method based on rational Gegenbauer func-
tions for solving boundary layer
ow of a PowellEyring non-Newtonian
uid, Computational and
Applied Mathematics, 37(5) 2018, 6053-6075
[26] K. Parand, M. Delkhosh, Operational matrices to solve nonlinear volterra-fredholm integro-differential
equations of multi-arbitrary order, Gazi University Journal of Science, 29(4) 2016, 895-907.
[27] K. Parand, M. Delkhosh, Solving Volterras population growth model of arbitrary order using the
generalized fractional-order of the Chebyshev functions Authors, Ricerche di Matematica, 65(1) 2016,
307-328.
[28] K. Parand, J.A. Rad, Numerical solution of nonlinear VolterraFredholmHammerstein integral equations via collocation method based on radial basis functions, Applied Mathematics and Computation,
218(9) 2012, 5292-5309.
[29] K. Parand, J.A. Rad, M. Nikarya, A new numerical algorithm based on the first kind of Modi ed
Bessel function to solve population growth in a closed system, International Journal of Computer
Mathematics, 91(6) 2014, 1239-1254.
[30] K. Paranda, M. Nikarya, A numerical method to solve the 1D and the 2D reaction diffusion equation
based on Bessel functions and Jacobian free Newton-Krylov subspace methods, The European Physical
Journal Plus 132(11) 2017, 1-18.
[31] K. Parand, S. Lati , M.M. Moayeri, M. Delkhosh, Generalized Lagrange Jacobi Gauss-Lobatto
(GLJGL) Collocation Method For Solving Linear and Nonlinear Fokker-Planck equations, Communi-
cations in Theoretical Physics, 69(5) 2018, 519.
[32] J. Radlow, A two-dimensional singular integral equation of diffraction theory, Bulletin of the American
Mathematical Society, (70)4 1964, 596-599.
[33] Y. Saad, M.H. Schultz, GMRES: A generalized minimal residual algorihm for solving nonsymmetric
linear system, SIAM Journal on scienti c and statistical computing, 7(3) 1986, 856-869.
[34] A. Soulaimani, N.B. Salah, Y. Saad, Enhanced GMRES acceleration techniques for some CFD prob-
lems, International Journal of Computational Fluid Dynamics, 16(1) 2002, 1-20.
[35] J. Shen, T. Tang, L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer
Publishing Company, Incorporated, 2011.
[36] S.C. Shiralashetti, R.A. Mundewadi, S.S. Naregal, B. Veeresh, Haar Wavelet Collocation Method
for the Numerical Solution of Nonlinear Volterra-Fredholm-Hammerstein Integral Equations, Global
Journal of Pure and Applied Mathematics, 13(2) 2017, 463-474.
[37] M.S. Tong, A Stable Integral Equation Solver for Electromagnetic Scattering by Large Scatterers with
Concave Surface, Progress In Electromagnetics Research, 74 2007, 113-130.
[38] E. Voltchkova, Integro-Differential Equations for Option Prices in Exponential Lvy Models, Finance
and Stochastics, 9(3) 2005, 299-325.
[39] P. Wolfe, Eigenfunctions of the Integral Equation for the Potential of the Charged Disk, Journal of
Mathematical Physics, 12(7) 1971, 1215-1218.
[40] S. Youse , M. Razzaghi, Legendre wavelets method for the nonlinear VolterraFredholm integral equa-
)