Numerical solution of stochastic integral equations by using Bernoulli operational matrix

Abadon, 2003, Fredholm-Volterra integral equation with singular kernel, App. Math. Comput., 137, 231, 10.1016/S0096-3003(02)00046-2 Abramowitz, 1972 Akyuz-Dascioglu, 2011, A Chebychev polynomial approach for linear Fredholm-Volterra integro-differential equations in most general form, Appl. Math. Comput. Sci., 3 Aleman, 2012, The eigenfunctions of the Hilbert matrix, 353 Arnold, 1974 Asari, 2014, Numerical solution of nonlinear stochastic integral equations by stochastic operational matrix based on Bernstein polynomials, Bull. Math. Soc. Sci. Math. Roumanie., 57, 3 Babolian, 2008, Direct method to solve volterra integral equation of the first kind using operational matrix with block-pulse functions, J. Comput. Appl. Math., 220, 51, 10.1016/j.cam.2007.07.029 Balachandran, 2010, Existence of solutions on nonlinear stochastic volterra fredholm integral equations of mixed type, Int. J. Math. Math. Sci., 10.1155/2010/603819 Bazm, 2015, Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations, J. Comput. Appl. Math., 275, 44, 10.1016/j.cam.2014.07.018 Bhrawy, 2012, A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals, Appl. Math. Comput., 219, 482 Brunner, 1989, The numerical solution of two-dimensional volterra integral equations by collocation and iterated collocation, IMA J. Numer. Anal., 9, 47, 10.1093/imanum/9.1.47 Guoqiang, 1993, Asymptotic error expansion variation of a collocation method for Volterra-Hammerstein equations, J. Appl. Numer. Math., 13, 357, 10.1016/0168-9274(93)90094-8 Higham, 2001, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43, 525, 10.1137/S0036144500378302 Kloeden, 1992 Kreyszig, 1978 Kumar, 1987, A new collocation-type method for Hammerstein integral equations, J. Math. Comput., 48, 123, 10.1090/S0025-5718-1987-0878692-4 Lehmer, 1998, A new approach to Bernoulli polynomials, Amer. Math. Monthly, 95, 905, 10.1080/00029890.1988.11972114 Maleknejad, 2012, Computational method based on Bernstein operational matrices for nonlinear Volterra–Fredholm– Hammerstein integral equations, Commun. Nonlinear Sci. Numer. Simul., 17, 52, 10.1016/j.cnsns.2011.04.023 Maleknejad, 2007, Numerical solution of the Volterra type integral equation of the first kind with wavelet basis, Appl. Math. Comput., 194, 400 Maleknejad, 2011, Modification of block pulse functions and their application to solve numerically Volterra integral equation of the first kind, Commun. Nonlinear Sci. Numer. Simul., 16, 2469, 10.1016/j.cnsns.2010.09.032 Milstein, 1995 Mirzaee, 2014, A collocation technique for solving nonlinear Stochastic Itô-Volterra integral equation, Appl. Math. Comput., 247, 1011 Mirzaee, 2018, Euler polynomial solutions of nonlinear stochastic Itô-Volterra integral equations, J. Comput. Appl. Math., 330, 574, 10.1016/j.cam.2017.09.005 MuskHelishvili, 1953 Natalini, 2003, A generalization of the Bernoulli polynomials, J. Appl. Math., 3, 155, 10.1155/S1110757X03204101 Nemati, 2015, Numerical solution of Volterra-Fredholm integral equations using Legendre collocation method, J. Comput. Appl. Math., 278, 29, 10.1016/j.cam.2014.09.030 Par, 2012, Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions, Appl. Math. Comput., 218, 5292 Srivastava, 2001 Tian, 2001, Implicit Taylor methods for stiff stochastic differential equations, App. Numer. Math., 38, 167, 10.1016/S0168-9274(01)00034-4 Tohidi, 2013, A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation, Appl. Math. Model., 37, 4283, 10.1016/j.apm.2012.09.032 Toutounian, 2013, A new Bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis, Appl. Math. Comput., 223, 298