We have suggested the numerical schemes of collocation methods and mechanical quadrature methods for approximative solution of singular integro-differential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on the descritization by Fejér points. Theoretical background for collocation method...

We present a novel design for quadrature phase detection utilizing two-mode optical waveguides for optical interferometric systems. A pair of interferometric signals having quadrature optical phase information can be obtained from the near-field and far-field patterns of a two-mode waveguide output. The operational principle is based on a pi/2 differential phase shift between two modal beams oc...

Plates and shells are significant structural components in many engineering and industrial applications. In this study, the free vibration analysis of annular plates is investigated. To this aim, two different numerical methods including the differential quadrature and the discrete singular convolution methods are performedfor numerical simulations. Moreover, the Frequency values are obtained v...

In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the nu...

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtai...

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increas...

Generalized Fitzhugh– Nagumo equation; Polynomial differential quadrature method; Numerical solutions; Runge–Kutta method Abstract In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order...