In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

In this paper, we show that the residual can be used to estimate the error of a numerical solution for a class of nonlinear Hammerstein equations. It is also shown that the superconvergence of the iterated numerical solution provides a sufficient condition for the residual to be used as an error estimator. Hammerstein equations with smooth as well as wekly singular kernels will be treated.

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

in this work, we present a numerical method for solving nonlinear fredholmand volterra integral equations of the second kind which is based on the useof block pulse functions(bpfs) and collocation method. numerical examplesshow eciency of the method.

In this paper we characterize viscosity solutions to nonlinear parabolic equations (including Monge-Ampere equations) by asymptotic mean value formulas. Our formulas can be interpreted from a probabilistic point of view in terms Dynamic Programming Principles for certain two-player, zero-sum games.

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...

Abstract The functional equations, functional integral equations and functional differential equations have many applications in nonlinear analysis. Also, the fractional order integral equations and fractional order differential equations have many applications in mathematical physics. Here we study the existence of solutions of a functional integral equations of arbitrary (fractional) order in...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...