Abstract: The aims of this study are to introduce acceleration methods that are called triangular acceleration methods, which come within the series of several acceleration methods that generally known as Al-Tememe's acceleration methods of the second kind which are discovered by (Ali Hassan Mohammed). These methods are useful in improving the results of determining numerical integrals of continuous integrands where the main error is of the forth order with respect to accuracy, partial intervals and the fasting of calculating the results (...) specifically to accelerate results come out by Simpson's method. Also, it is possible to make use of it to improve the results of solving differential equations numerically of the main error of the forth order. (shrink)

Abstract: The aims of this study are to introduce acceleration methods that called relative and algorithmic acceleration methods, which we generally call Al-Tememe's acceleration methods of the second kind discovered by (Ali Hassan Mohammed). It is very useful to improve the numerical results of continuous integrands in which the main error is of the 4th order, and related to accuracy, the number of used partial intervals and how fast to get results especially to accelerate the results got by Simpson's method. (...) Also, it is possible to utilize it in improving the results of differential equations numerically of the main error of the forth order. (shrink)

Abstract: The main aim of this work is to introduce acceleration methods called a Trigonometric acceleration methods which are of series of numerated methods. In general, these methods named as AL-Tememe’s acceleration methods of first kind to his discoverer ''Ali Hassan Mohammed''. These are very beneficial to acceleration the numerical results for definite integrations with continuous integrands which are of 2nd order main error, with respect to the accuracy and the number of the used subintervals and the fasting obtaining results. (...) Especially, for acceleration the results which are obviously obtained by trapezoidal and midpoint methods. Moreover, these methods could be enhancing the results of the ordinary differential equations numerically which are of 2nd order main error. (shrink)

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