Numerical differentiation for high orders by an integration method

A Numerical Integration Method by Using Generalized Series of Functions

a numerical integration method by using generalized series of functions

New Iterative Methods for Interpolation, Numerical Differentiation and Numerical Integration

Through introducing a new iterative formula for divided difference using Neville's and Aitken's algorithms, we study new iterative methods for interpolation, numerical differentiation and numerical integration formulas with arbitrary order of accuracy for evenly or unevenly spaced data. Basic computer algorithms for new methods are given.

An Improved Numerical Integration Method for Flight Simulation

In this paper a modified form of Euler integration is described which, when applied to the six-degree of freedom flight equations, retains and enhances many of the advantages of AB-2 integration and at the same time eliminates the disadvantages. The scheme is based on the Euler integration formula, but with the state-variable derivative represented at the midpoint of each integration step. In t...

An Iterative Method for Numerical Integration of Rational Functions

We describe a new method for numerical integration of rational functions on the real line. Given a rational integrand, we provide a new rational function preserving its integral on the line. The coefficients of the new function are explicit polynomials in the original ones. These transformations depend on the degree of the input and the desired order of the method. Both parameters are arbitrary...