in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

in this paper, the two-dimensional triangular orthogonal functions (2d-tfs) are applied for solving a class of nonlinear two-dimensional volterra integral equations. 2d-tfs method transforms these integral equations into a system of linear algebraic equations. the high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one t...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing to ch...

In this work we extend the results of [2] to a family of abstract functionals of autonomous type satisfying suitable locality and additivity properties, and general integral growth conditions of superlinear type. We single out a condition which is necessary and sufficient in order for a functional of this class to admit an integral representation, and sufficient as well to have an integral repr...

Using a circular contour integral representation for the generalized Marcum-Q function, ( ), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagamifading with positive integer fading severity index. This result involves only elementary functions and holds for any value...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. By integrating two of the four dimensions analytically, the coincident integration, deened as a limit to the boundary, is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in...

The rapidly growing amount of genomic sequence data being generated and made publicly available necessitate the development of new data storage and archiving methods. The vast amount of data being shared and manipulated also create new challenges for network resources. Thus, developing advanced data compression techniques is becoming an integral part of data production and analysis. The HapMap ...

The linear integral equation based computer code (RON: “Roger Oleg Nikolai”), which was recently developed at Argonne National Laboratory, was used to calculate the self-amplified spontaneous emission (SASE) performance of the free-electron laser (FEL) being built at Argonne. Signal growth calculations under different conditions are used for estimating tolerances of actual design parameters. Th...

In this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice Z with nearest neighbor hopping rates p to the right and q = 1−p to the left. For the most part we consider an N -particle system but for certain of these formulas we can take the N → ∞ limit. First we obtain, for the N -particle system, a formula for the ...