An Efficient Tri-Parametric Jarratt Family for Nonlinear Models Solution - Ogbereyivwe, O.; Emumejaye, K.; Umar, S. S. (Communications in Mathematics and Applications, 2024)
This paper offers an efficient and competitive tri-parametric family of iterative schemes for deciding nonlinear and systems of nonlinear models solution. The family has quartic-convergence 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.
Keywords: Nonlinear model; Iterative scheme; Jarratt’s scheme; Rational approximation function; Convergence order