the main purpose of this article is to increase the efficiency of the least squares method in numerical solution of ill-posed functional and physical equations. determining the least squares of a given function in an arbitrary set is often an ill-posed problem. in this article, by defining artificial constraint and using lagrange multipliers method, the attempt is to turn -dimensional least squ...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

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...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

on the basis of the steady-state two-dimensional theory of thermoelasticity, stress field around various holes in infinite isotropic plate is discussed. the plate is subjected to uniform heat flux and thermal insulated condition along the hole boundary is assumed. by using the complex potential functions and by applying the conformal mapping and solving the integral equations, the effect of blu...

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...

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...

This paper presents a study on estimation of heat transfer coefficient and thermal diffusivity parameters by use of analytical solutions and experimental data for regular geometries (infinite slab, infinite cylinder and sphere). Analytical solutions have a broad use in experimentally determining these parameters. These solutions, with use of experimental data, might give a greater advantage ove...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.