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

Authors : Tugal ZHANLAV, R MİJİDDORJ, Otgondorj KHUDER

Pages : 1006-1021

Doi:10.15672/hujms.1061471

View : 138 | Download : 256

Publication Date : 2023-08-15

Article Type : Research Paper

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