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.

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...

In this paper we study systems of the form b ≤ Mx ≤ d, l ≤ x ≤ u, where M is obtained from a totally unimodular matrix with two nonzero elements per row by multiplying by 2 some of its columns, and b, d, l, u are integral vectors. We give an explicit description of a totally dual integral system that describes the integer hull of the polyhedron P defined by the above inequalities. Since the ine...

Let A be a rational (m x n)-matrix and b be a rational m-vector. The linear system Ax< b is said to be totally dual integral (TDI) if for all integer n-vectors c, the linear program min{b’v: A’y= c; yr 0} has an integer-valued optimum solution if it has an optimum solution. The contents of this paper can be divided into three parts: First of all an attempt is made to characterize special classe...

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar’s integral equation. In ...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...