Large-scale networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to ascertain the ease of traveling between nodes. These and related quantities can be determined by evaluating expressions of the form u T f (A)w, where A is the adjacency matrix that represents the graph of the network, f is a nonlinear function, such as the ...

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

In this paper we examine the computation of the potential generated by space-time BIE representations associated with Dirichlet and Neumann problems for the 2D wave equation. In particular, we consider the efficient evaluation of the (convolution) time integral that appears in the potential representation. For this, we propose two simple quadrature rules which appear more efficient than the cur...

The aim of the present paper is to find efficient method computation wave-making resistance a ship using mitchell’s integral. computational schemes described in publications suggest use simple quadratures (trapezoidal and Simpson’s rule) with fixed number integration’s intervals. This approach assumes manual setup algorithm for calculating each new makes it difficult estimate error obtained res...

This paper first presents a Gauss Legendre quadrature method for numerical integration of I 1⁄4 R R T f ðx; yÞdxdy, where f(x,y) is an analytic function in x, y and T is the standard triangular surface: {(x,y)j0 6 x, y 6 1, x + y 6 1} in the Cartesian two dimensional (x,y) space. We then use a transformation x = x(n,g), y = y(n,g) to change the integral I to an equivalent integral R R S f ðxðn;...

Orthogonal polynomials, unless they are classical, require special techniques for their computation. One of the central problems is to generate the coefficients in the basic three-term recurrence relation they are known to satisfy. There are two general approaches for doing this: methods based on moment information, and discretization methods. In the former, one develops algorithms that take as...