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...

This paper presents the solution to the following optimization problem: What is the shape of the region that minimizes the average Lp distance between all pairs of points if the area of this region is held fixed? (The Lp-distance between two points x = (x1, x2) and y = (y1, y2) in < 2 is (|x1 − y1| p + |x2 − y2| p).) We use variational methods to determine the shape of the region that minimizes...

We consider a class of potential problems on a periodic half-space for the modeling of electrified oil films, which are used in the development of novel switchable liquid optical devices (diffraction gratings). A boundary integral formulation which reduces the problem to the study of the oil-air interface alone is derived and solved in a highly efficient manner using the Nyström method. The oil...

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.

Isogeometric analysis is applied to boundary integral equations corresponding to boundary-value problems governed by Laplace’s equation. It is shown that the smoothness of geometric parametrizations central to computer-aided design can be exploited for regularizing integral operators. As a result, one obtains high-order collocation methods based on superior approximation and numerical integrati...

The solution of eigenvalue problems for partial differential operators by using boundary integral equation methods usually involves some Newton potentials which may be resolved by using a multiple reciprocity approach. Here we propose an alternative approach which is in some sense equivalent to the above. Instead of a linear eigenvalue problem for the partial differential operator we consider a...

Abstract. Starting from a recently developed energetic space-time weak formulation of boundary integral equations related to wave propagation problems defined on single and multidomains, a coupling algorithm is presented, which allows a flexible use of finite and boundary element methods as local discretization techniques, in order to efficiently treat unbounded multilayered media. Partial diff...

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The...

As stated in an Chapter 4, prokaryotes of both Domains or Superkingdoms, the Bacteria and the Archaea, mediate the formation of a large number of diverse minerals. They are known to do this either through biologically induced mineralization (BIM) (Lowenstam 1981) (the subject of Chapter 4 in this volume; Frankel and Bazylinski 2003) or biologically controlled mineralization (BCM). The latter ha...

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.