In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

In this paper a numerical method for finding the solution of FredholmHammerstein integral equations is proposed. At first the properties of the Walsh-hybrid functions, which combination of block-pulse functions and Walsh functions are proposed. The properties of the hybrid functions with the operational matrix of integration together Newton-Cotes nodes are then utilized to reduce the solution o...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The para...

As an extension of the Leray-Schauder degree, we introduce a topological degree theory for a class of demicontinuous operators of generalized (S+) type in real reflexive Banach spaces, based on the recent Berkovits degree. Using the degree theory, we show that the Borsuk theorem holds true for this class. Moreover, we study the Dirichlet boundary value problem involving the p-Laplacian by way o...

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bou...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...