A family of runge-kutta-like iterative procedure for solution of nonlinear algebraic models

Nonlinear models that are algebraic in nature are often encountered in diverse areas of science and engineering, often requiring efficient numerical methods for their precise solutions. Newton and Householder methods, being among the classical methods, may experience slow convergence or require expensive evaluation of derivative, which is costly, thus encouraging the development of alternative approaches. Motivated by the Householder method’s convergence and precision structure, this paper put forward a newfamily of third-order Runge-Kutta-like procedure iterative methods. By leveraging on divided difference, a concrete member of the proposed family is enhanced for higher convergence and precision without needing the assessment of higher derivative evaluation, developing a fifth-order convergence method. The theoretical convergence of the methods was established via the use of the Taylor series expansion. To demonstrate the efficacy of the proposed methods, they were tested on recent models in engineering,science and environment, and their performance was compared with some existing methods of the same order of convergence. The test results indicate that the proposed methods performed better than the compared method in many cases, in terms of the metrics used for comparison.

کلیدواژه ها:

Runge-Kutta method ، Householder method ، Nonlinear algebraic model ، iterative method