In this paper we present a new approach for linear Volterra integral equations that is based on optimal control theory. Some optimal control problems corresponding Volterra integral equation be introduced which we solve these problems by discretization methods and linear programming approaches. Finally, some examples are given to show the efficiency of approach. Index Terms —Volterra integral e...

In the recent years, a new attention has been given to reaction-diffusion systems which involve an integral over the spatial domain of a function of the desired solution on the boundary conditions; see [2, 5, 7, 6, 9, 10, 17, 18, 19, 20, 22] and the references cited therein. Most of the studied problems in the current literature are devoted to problems which combine a classical boundary conditi...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established f...

Fuzzy integral equations play major roles in various areas, therefore a new method for finding a solution of the Fredholm fuzzy integral equation is presented. This method converts the fuzzy integral equation into linear system by using the Taylor series. For this scope, first the Taylor expansion of unknown function is substituted in parametric form of the given equation. Then we differentiate...

We present a computational methodology (a novel Nyström approach based on use of a non-overlappingpatch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Fie...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.