The weak Neumann problem for the Poisson eqution is studied on Lipschitz domain with compact boundary using the direct integral equation method. The domain is bounded or unbounded, the boundary might be disconnected. The problem leads to a uniquely solvable integral equation in H(∂Ω). It is proved that we can get the solution of this equation using the successive approximation method. AMS class...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of openboundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time. PACS. 41.20.Cv Electrostatics; Poisson and Laplace equatio...

∂u ∂t = A ∂ 2 u ∂x2 , u(0, x) = g(x). Moreover, we consider a representation of the solution of this problem as a Poisson integral and study the Cauchy problem for the corresponding inhomogeneous equation. Bibliography: 22 titles.

The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a ...