Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. The later has become one of the most popular numerical schemes in recent years. In this expository paper, we discuss some of the essential features of the methods, their intimate relations with the variatio...

boundary integral equations (bie) are reformulations of boundary value problems for partial differential equations. there is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. in this paper, the neumann problem is reformulated to a bie, and then moving least squares as a meshless method is describe...

Third-order boundary-value problems for differential equation play a very important role in a variety of different areas of applied mathematics and physics. Recently, third-order boundary-value problems have been many scholars’ research object. For example, heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics can produce boundary-value problems wit...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

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.

in this paper, the optimal boundary control problem for distributed parabolic systems, involving second orderoperator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. some specific properties of the optimal control arediscussed.

in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

In this article, we apply this new method for solving an engineering systemwith initial and boundary conditions and integral criterion ,and we will usingdynamic programming as iteration for solving model.

This paper is concerned with the efficient evaluation of some highly oscillatory surface integrals, arising from boundary integral methods for high frequency acoustic scattering in three dimensions. The performance of standard quadrature schemes deteriorates as the frequency of the incident wave increases. We present ideas for improving the evaluation of such highly oscillatory integrals. Intro...