New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations

作者：Narang Mona; Bhatia Saurabh; Kanwar Vinay^*

来源：Numerical Algorithms, 2017, 76(1): 283-307.

DOI：10.1007/s11075-016-0254-0

• Systems of nonlinear equations
• Order of convergence
• Steffensen's method
• Higher order methods
• Computational efficiency

We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations.

• 出版日期2017-9