In this study, we suggest and analyze a new and wide general class of Jarratt’s method for solving systems of nonlinear equations. These methods have fourth-order convergence and do not require the evaluation of any second or higher-order Fréchet derivatives. In terms of computational cost, all these methods require evaluations of one function and two first-order Fréchet derivatives. The performance of proposed methods is compared with their closest competitors in a series of numerical experiments. It is worth mentioning that all the methods considered here are found to be effective and comparable to the robust methods available in the literature.
Kanwar, V.; Kumar, Sanjeev; and Behl, Ramandeep
Several New Families of Jarratt’s Method for Solving Systems of Nonlinear Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
2, Article 23.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss2/23