In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

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...

As for most Diophantine equations, quadratic forms were first studied over the integers, meaning that the coefficients aij are integers and only integer values of x1, . . . , xn are allowed to be plugged in. At the end of the 19th century it was realized that by allowing the variables x1, . . . , xn to take rational values, one gets a much more satisfactory theory. (In fact one can study quadra...

<p style='text-indent:20px;'>This paper is concerned with a linear quadratic optimal control for class of singular Volterra integral equations. Our framework covers the problems fractional differential Under some necessary convexity conditions, an exists, and can be characterized via Fréchet derivative functional in Hilbert space or maximum principle type conditions. However, these (equiv...

In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation inverse operators that appear solution Fredholm integral equations. Therefore, construct iterative with quadratic convergence does not use either derivatives or operators. Consequently, new procedure is especially useful non-homogeneous first kin...