this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

Some features of functional and integral equations involved in the spectral approach developed by the author (in Qu. J. of Mech. and Appl. Math., 59, 4, pp.517-550, 2006) for scattering by two-dimensional polygonal objects with arbitrary surface impedance conditions are presented. In this problem, the Wiener-Hopf method cannot be applied, while asymptotic methods can only be used if corners are...

We give a realization of the Beisert, Eden and Staudacher equation for the planar N = 4 supersymetric gauge theory which seems to be particularly useful to study the strong coupling limit. We are using a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into to a syst...

Preface In our course we will consider the volume integral equations in the following form) () () () () () (x f dy y u y b y x y x K x u x a Q m = − − + ∫ , 3 ≤ m. Many important classes of the wave scattering problems can be described by equations of this form; for example, this is the case for problems of electromagnetic and acoustic scattering on 3D transparent bodies. The corresponding inte...

Using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations whi...

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...