A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear m...

The main purpose of this article is to demonstrate the use of the two Dimensional Walsh and Haar functions with Operational Matrix for solving nonlinear Volterra-Fredholm integral equations. The approximate solution is represented in the form of series. The approximate solution is obtained by two Dimensional Walsh and Haar series. The operational matrix and direct method for solving the linear ...

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples. Keywor...

Monte Carlo Algorithms for Solving Fredholm Integral Equations and Fredholm Differential Integral Equations Behrouz Fathi Vajargah and Mojtaba Moradi Department of Mathematics Guilan University, Rasht, Iran [email protected], [email protected] Abstract In this paper we establish a new algorithm for solving non linear differential integral equations based on Monte Carlo methods. For obta...

We use the canonical Lipschitz geometry available on the boundary of a hyperbolic group to construct finitely summable Fredholm modules over the crossed product of the boundary action. The procedure yields a full set of representatives of the K-homology of the crossed product, and all of them are p-summable for p in an appropriate range related to the geometry of the boundary. By restricting th...

We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension, the half-line is re...

We shall study smooth maps ~ u : _ S ! RM of nite energy deened on the punctured Riemann surface _ S = S n? and satisfying a Cauchy-Riemann type equation T ~ u j = J(~ u) T ~ u for special almost complex structures J, related to contact forms on the compact three manifold M. Neither the domain nor the target space are compact. This diiculty leads to an asymptotic analysis near the punctures. A ...

We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is rep...

We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is rep...

We discuss several natural metrics on spaces of unbounded self– adjoint operators and their relations, among them the Riesz and the graph metric. We show that the topologies of the spaces of Fredholm operators resp. invertible operators depend heavily on the metric. Nevertheless we prove that in all cases the spectral flow is up to a normalization the only integer invariant of paths which is pa...