in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

Various authors have considered the Zero-rest-mass equation and the contour integral representation of its solutions. Ferber generalized these equations to supertwistor spaces with 2N odd components so that with N=O we get the standard ungraded twistors of Penrose. In this paper we use the Batchelor theorem toconstruct the natural super Twistor space with coarse topology with underlying sta...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

where  < λ < n,  < β + λ < n, and p,q, r ≥  satisfying p + q + r = (n – λ – β)/λ. Recently, there has been tremendous interest in studying integral systems. Because the integral equation(s) not only formulate abstractly many laws and relations in science, engineering, economics, and other fields of applied science, but also they provide a special technique to investigate the global propert...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

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.

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, an iterative scheme for extracting approximate solutions of two dimensional volterra-fredholm integral equations is proposed. considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. several examples are provided to demonstrate the effc...

Consider the second-order nonlinear dynamic equation [r(t)x(ρ(t))] + p(t)f(x(t)) = 0, where p(t) is the backward jump operator. We obtain a Kwong-Wong-type integral equation, that is: If x(t) is a nonoscillatory solution of the above equation on [T0,∞), then the integral equation rσ(t)x∆(t) f(xσ(t)) = P(t) + Z ∞ σ(t) rσ(s)[ R 1 0 f (xh(s))dh][x ∆(s)]2 f(x(s))f(xσ(s)) ∆s is satisfied for t ≥ T0,...