the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. we discuss also the existence of a solution to a nonlinear random integral equation in banah spaces.

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...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...

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...

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...

in this paper, we present a numerical method for solving nonlinear fredholm and volterra integral equations of the second kind which is based on the use of haar wavelets and collocation method. we use properties of block pulse functions (bpf) for solving volterra integral equation. numerical examples show efficiency of the method.

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.