In this work, we tried to find the inverse coefficient in the Euler problem with over determination conditions. It showed the existence, stability of the solution by iteration method and linearization method was used for this problem in numerical part. Also two examples are presented with figures.

We use a spectral transform method to study general boundary-value problems for thirdorder, linear, evolution partial differential equations with constant coefficients, posed on a finite space domain. We show how this method yields a simple characterization of the discrete spectrum of the associated spatial differential operator, and discuss the obstructions that arise when trying to represent ...

In this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. The conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. This study evaluates the advantages of using the integral form of the equations in the...

The mechanism for the generation of vorticity at a viscous free surface is described. This is a free-surface analogue of Lighthill’s strategy for determining the vorticity flux at solid boundaries. In this method the zero-shear-stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity– vorticity description of the flow. A vortex sheet...

We study the classical generalized gln Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl2 L-L model. Novel expressions of the modified Lax pairs associated to the integrals of motion are also extracted. The relevant equations of mo...

We consider the Laplace problem in a three-dimensional domain with a straight-edge singularity caused by two intersecting flat planes. The solution in the neighbourhood of such edge can be expressed as an asymptotic expansion involving the eigenpairs of the analogous two-dimensional problem in polar coordinates, which have as coefficients the so-called edge flux stress intensity functions (EFIF...

One-dimensional parabolic equation; Nonlocal boundary conditions; Taylor approximation; Operational matrices; Krylov subspace iterative methods; Restarted GMRES Abstract This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs) subject to nonlocal boundary integral c...

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...

Using the Gauss linking integral we define a new measure of entanglement for a collection of closed or open chains, the linking matrix. For a system employing periodic boundary conditions (PBC) we use the periodic linking number and the periodic selflinking number to define the periodic linking matrix. We discuss its properties with respect to the cell size used for the simulation of a periodic...

Abstract. In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the LieTrotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given either with per...