An efficient tri-parametric Jarratt family for nonlinear models solution
Abstract
This paper offer an efficient and rivalrous tri-parametric family of iterative schemes for
nonlinear and system of nonlinear models solution approximation. The family has quarticconvergence order and is based on the composition of the Jarratt’s perturbed Newton method
with a designed iterative function that involves rational approximation function of degree two
in both its denominator and numerator. The new tri-parametric family is further extended to
solving nonlinear models in n-dimensional form and its convergence investigation established
to retain its quartic-convergence order. By varying the parameters in the family, enabled the
rediscovery of many well established iterative schemes. The applicability and computational
performance of some specified family examples, on some nonlinear models were also verified
and results compared with some of known and established schemes that are also family
members.
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