This paper presents an algebraic method that uses the triangular factors of singular, symmetric gain matrix to determine the observable islands of a measured power system. This is accomplished in a noniterative manner via the use of selected rows of the inverse factors. Implementation of the proposed method presents little additional effort, since sparse triangular factorization and forward/bac...

This paper studies inference on nondifferentiable functions using methods based on numerical differentiation. First we show that for an appropriately chosen sequence of step sizes, numerical derivative based delta methods provide consistent inference for functions of parameters that are directionally differentiable. Examples of directionally differentiable functions arise in a variety of econom...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

A new method is given for eeecting numerical diierentiation by means of an optimization procedure. The method is shown to be eeective for the diierentiation of noisy functions, and stability and convergence results for a steepest descent implementation are proved.

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, and Wilson, and uses Evans and Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one di...

We use the bivariate spline method to solve the steady state Navier-Stokes equations numerically. The bivariate spline we use in this paper is the space of splines of smoothness r and degree 3r over triangulated quadrangu-lations. The stream function formulation for the steady state Navier-Stokes equations is employed. Galerkin's method is applied to the resulting nonlinear fourth order equatio...

In the last decades, the interplay between increasing precision from the experimental side and NLO predictions becoming available from the theoretical side has led to impressive tests of the Standard Model. However, certain processes or observables in QCD should be known at NNLO in perturbation theory in order to match the experimental precision, and in the domain of electroweak interactions, m...

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear fuzzy equations using the Harmonic mean rule. We prove that this method has quadratic convergence. The fuzzy quantities are presented in parametric form. Sever examples are given to illustrate the efficiency of the proposed method. Mathematics Subject Classification: 03E72; 37C25