Using inverse triangular and hyperbolic functions of Al-Tememe acceleration methods of first kind for improving the numerical integration results

Abstract

The main aim of this work is to introduce the acceleration methods which are called the inverse triangular acceleration methods and inverse hyperbolic acceleration methods, which are considered a series of  numerated methods. In general, these methods are named as AL-Tememe’s acceleration methods of first kind discovered by (Ali Hassan Mohammed). They are very beneficial to acceleration the numerical results for definite integrations with continuous integrands which are of 2^nd order main error, with respect to the accuracy and the number of the used subintervals and the speed of obtaining results. Especially, for accelerating the results which are obviously obtained by trapezoidal and midpoint methods. Moreover, these methods could be enhancing the results of numerical of  the ordinary differential equations, where the main errors are of 2^nd order.