A family of Newton-type methods with seventh and eighth-order of convergence for solving systems of nonlinear equations

Year 2023, Volume: 52 Issue: 4, 1006 - 1021, 15.08.2023

Tugal Zhanlav , R. Mijiddorj , Otgondorj Khuder

https://doi.org/10.15672/hujms.1061471

Cited By: 5

Abstract

In this work, we first develop a new family of three-step seventh- and eighth-order Newton-type iterative methods for solving systems of nonlinear equations. We also propose some different choices of parameter matrices that ensure the convergence order. The proposed family includes some known methods as special cases. The computational cost and efficiency index of our methods are discussed. Numerical experiments are conducted to support the theoretical results.

Keywords

Nonlinear system, Newton-type method, seventh- and eighth-order convergence, computational efficiency

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