An optimal and efficient general eighth-order derivative free scheme for simple roots

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Behl, Ramandeep^1,2  Gonzalez, D.³  Maroju, Prashanth¹  Motsa, S. S.¹ 

[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-3209 Pietermaritzburg, South Africa

[2] King Abdulaziz Univ, Dept Math, Jeddah, Saudi Arabia

[3] Univ Amer, Escuela Ciencias Fis & Matemat, Quito 170125, Ecuador

关键词: Nonlinear equations;    Simple roots;    Computational order of convergence;    Steffensen's type method;   

DOI  :  10.1016/j.cam.2017.07.036

来源: Elsevier

【 摘 要 】

The main motivation of this study is to present an optimal scheme in a general way that can be applied to any existing optimal multipoint fourth-order iterative scheme whose first substep employs Steffensen's method or Steffensen like method to further produce optimal eighth-order iterative schemes. A rational function approximation approach is used in the construction of proposed scheme. In addition, we also discussed the theoretical and computational properties of our scheme. Each member of the presented scheme satisfies the optimality conjecture for multipoint iterative methods without memory which was given by Kung and Traub in 1970. Finally, we also concluded on the basis of obtained numerical results that our methods have faster convergence in contrast to the existing methods of same order because they have minimum residual errors, minimum error difference, between two consecutive iterations and minimum asymptotic error constants corresponding to the considered test function. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free