Scientists and engineers are mainly using Richardson extrapolation as a computational tool
for increasing the accuracy of various numerical algorithms for the treatment of systems of …

In this work, we propose a new n+ 1 integration scheme over arbitrary polygonal elements
based on centroid approximation and Richardson extrapolation scheme. For the purpose of …

An efficient, stable and accurate quadrilateral element and its improved stiffness matrix on
the midpoint quadrature concept is proposed in this research study. As a first approximation …

This paper investigates a two-dimensional Riemann–Liouville distributed-order space
fractional diffusion equation (RLDO-SFDE). However, many challenges exist in deriving …

The estimation of the discretization error via the Richardson extrapolation (RE) is considered
for problems with discontinuities (shock waves and contact lines) having the variable order …

The distance between the true and numerical solutions in some metric is considered as the
discretization error magnitude. If error magnitude ranging is known, the triangle inequality …

The estimation of a vicinity of the approximate solution that contains the exact one (exact
solution enclosure) may be performed using an ensemble of numerical solutions if the …

This research paper introduces a robust, efficient and stabilized midpoint quadrature to
generate element stiffness matrices for quadrilateral and hexahedral elements in finite …

In this paper, a new closed-form formulation with universal matrices strongly recommends
that Weighted Richardson Extrapolation (WRE) with robust and hourglass controlled one …

The consistency of the classical Richardson extrapolation (CRE), a simple and robust
computational device, is analysed for the case where the underlying method is an explicit …