‎in this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(vofides‎, ‎for short)‎. ‎in these equations‎, ‎the variable-order fractional integration(vofi) and‎ ‎variable-order fractional derivative (vofd) are described in the‎ ‎riemann-liouville's and caputo's sense,respectively‎. ‎numerical experiments‎, ‎consisting of two exam...

Numerical integration is the study of how the numerical value of an integral can be found. Also called quadrature, which refers to nding a square whose area is the same as the area under a curve, it is one of the classical topics of numerical analysis. Of central interest is the process of approximating a deenite integral from values of the in-tegrand when exact mathematical integration is not ...

Although exact analytical solutions to integrals are always desirable, such luxuries are rarely available when dealing with the real-world systems. Consequently, numerical integration has become an indispensable tool when evaluating complex designs, and it is far more common for engineers to obtain solutions numerically rather than through exact mathematical expressions. This can be especially ...

In the present paper we study quasi-Monte Carlo methods to integrate functions representable by generalized Haar series in high dimensions. Using (t; m; s)-nets to calculate the quasi-Monte Carlo approximation, we get best possible estimates of the integration error for practically relevant classes of functions. The local structure of the Haar functions yields interesting new aspects in proofs ...

We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculat...

Here we will begin by deriving the basic trapezoidal and Simpson’s integration formulas for functions that can be evaluated at all points in the integration range, i.e, there are no singularities in this range. We will also show how the remaining discretization errors present in these low-order formulas can be systematically extrapolated away to arbitrarily high order; a method known as Romberg...

micropolar plasticity provides the capability to carry out post-failure simulations of geo-structures due to microstructural considerations and embedded length scale in its formulation. an essential part of the numerical implementation of a micropolar plasticity model is the integration of the rate constitutive equations. efficiency and robustness of the implementation hinge on the type of inte...

A numerical dynamic-aerodynamic interface for simulating the separation dy­n­a­m­ic­s of co­n­­s­t­r­a­i­ned strap-on boosters jettisoned in the atmosphere is presented. A 6-DOF multi body dynamic solver ،using Constraint For­ce Equation Methodology is coupled with a numerical time dependent Euler flow solver. An automatic dyna­m­i­­c mesh updating proc­e­d­ure is employed using smoothing and l...

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.