Abstract The objective of this research is to study numerical integral equation method (NIE) using five quadrature rules namely, composite midpoint rule, trapezoidal Simpson’s Boole’s rule and Gauss-Legendre for approximating the average run length on extended exponentially weighted moving (extended EWMA) control chart autoregressive process with explanatory variables when white noise follows a...

Nyström method is a standard numerical technique to solve Fredholm integral equations of the second kind where integration kernel approximated using quadrature formula. Traditionally, rule used classical polynomial Gauss quadrature. Motivated by observation that given function can be better spline lower degree than single piece higher degree, in this work, we investigate use Gaussian rules for ...

A new adaptive quadrature algorithm that places a greater emphasis on cost reduction while still maintaining an acceptable accuracy is demonstrated. The different needs of science and engineering applications are highlighted as the existing algorithms are shown to be inadequate. The performance of the new algorithm is compared with the well known adaptive Simpson, Gauss-Lobatto and GaussKronrod...

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order 2 > 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic s...

We propose a mixed finite element method for Stokes flow with one degree of freedom per and facet simplicial grids. The is derived by considering the vorticity-velocity-pressure formulation eliminating vorticity locally through use quadrature rule. discrete solution pointwise divergence-free pressure robust. theoretically convergence rates are confirmed numerical experiments.

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative stud...

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...

Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependen...