Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation

• DOI: 10.3390/math7020164
• Publication Date: 2019-02-13T07:49:44Z
• Authors: Moin-ud-Din Junjua; Fiza Zafar; Nusrat Yasmin
• Keywords: Interpolation; Derivative (finance); Root (linguistics); Root-finding algorithm

Finding a simple root for nonlinear equation f ( x ) = 0 , : I ⊆ R → has always been of much interest due to its wide applications in many fields science and engineering. Newton’s method is usually applied solve this kind problems. In paper, such problems, we present family optimal derivative-free finding methods arbitrary high order based on inverse interpolation modify it by using transformation first derivative. Convergence analysis the modified confirms that convergence preserved according Kung-Traub conjecture. To examine effectiveness significance newly developed numerically, several equations including van der Waals are tested.