Inverse Triangular and Hyperbolic Acceleration Methods of Second Kind for Improving the Numerical Integration Results

Abstract

The aims of this study are to introduce the acceleration methods which are called inverse triangular acceleration methods and inverse hyperbolic triangular acceleration methods, which we generally call Al-Tememe's acceleration methods of the second  kind discovered by (Ali Hassan Mohammed). It is useful to improve the numerical results of continuous integrals in which the error is of the 4^th order, and regarding to accuracy, the number of used partial intervals and how fast is to get results especially to accelerate the results that can be got by using Simpson's method. Also, it is possible to utilize it in improving the numerical results of differential equations ,where the main error  is of the forth order.