New Iterative Methods for Interpolation, Numerical Differentiation and Numerical Integration

TL;DR

This paper introduces new iterative algorithms for interpolation, differentiation, and integration that achieve arbitrary accuracy levels for both evenly and unevenly spaced data, enhancing computational methods.

Contribution

It presents novel iterative formulas based on Neville's and Aitken's algorithms for improved numerical methods with arbitrary order accuracy.

Findings

Developed new iterative formulas for divided differences.

Achieved arbitrary order accuracy for interpolation, differentiation, and integration.

Provided basic algorithms for practical implementation.

Abstract

Through introducing a new iterative formula for divided differnce 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 evanly or unevanly spaced data. Basic computer algorithms for new methods are given