يك روش بهينه جديد از همگرايي مرتبه 4 براي حل معادلات غير خطي

در اين مقاله يك روش مرتبه چهار براي محاسبه ريشه هاي ساده از معادلات غير خطي با استفاده از روش تيلر و تقريب تابع وزن ارايه مي دهيم. روش ارايه شده بر مبناي روش فرناندو-ويراكون مي باشد.

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon- Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newtonʹs method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate, namely one evaluation of function and two evaluations of rst derivative. So, Kung and Traubʹs conjecture is fulfilled. We also perform some numerical tests that conrm the theoretical results and allow us to compare the proposed method with some existing methods of the same type.