A Modified Twentieth-Order Iterative Method for Solving Nonlinear Physicochemical Models: Convergence, Physical Models and Basin of Attraction Analysis
DOI:
https://doi.org/10.53560/PPASA(62-4)699Keywords:
Nonlinear Physicochemical Models, Iterative Method, Convergence Analysis, Weight Function, Hermite Interpolation, Basin of AttractionAbstract
This paper introduces a modified twentieth-order method for solving nonlinear equations that commonly arise in physicochemical models. The proposed method is designed to efficiently handle the complex problems that normally occur in the van der Waals equation for real gases, Planck’s radiation law, and chemical equilibrium conditions. The traditional method has a lower order of convergence and uses higher-order derivatives. However, proposed method has twentieth-order convergence with only one first derivative used in each iteration. A detailed convergence order has been carried out to demonstrate the theoretical order of accuracy. Various numerical experiments have also been carried out to validate the performance of the proposed method. The results show the significantly improve the accuracy and taking a smaller number of iterations, number of function evaluations, and CPU time when applied to nonlinear equations arises in van der Waals equation for real gases, Planck’s radiation law, and chemical equilibrium conditions and basin of attraction further validate the stability of proposed method.
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