Novel Alternative Methods to Romberg Integration and Richardson’s Extrapolation with Matlab Package:Integral_Calculator

Abstract

This paper introduces new integration methods for numerical integration problems in science and engineering applications. It is shown that the exact results of these integrals can be obtained by these methods with the use of only 2 segments. So no additional function and integrand evaluations are required for different levels of computation. This situation overcomes the computational inefficiency. A new Matlab Package; Integral_Calculator is presented. Integral_Calculator provides a user-friendly computational platform which requires only 3 data entries from the user and performs the integration and give the results for any functions to be integrated. This package has been tested for each numerical example considered below.