Analysis of optimal iterative methods from a dynamical point of view by studying their stability properties

• Published in: Journal of mathematical chemistry Vol. 62; no. 1; pp. 198 - 221
• Main Authors: Kansal, Munish, Sharma, Himani
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2024; Springer Nature B.V
• Subjects: Chemical reactors; Chemistry; Chemistry and Materials Science; Dynamic stability; Iterative methods; Math. Applications in Chemistry; Original Paper; Physical Chemistry; Stability analysis; Theoretical and Computational Chemistry; 65B99; Nonlinear equation; Stability; Iterative method; Complex dynamics; Dynamical plane; 65H05
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-023-01523-2

In this work, we carry out the dynamical analysis of a proposed optimal fourth-order iterative family of methods in the complex plane that allows us to find those parametric values for which the corresponding family variant’s behavior is stable or unstable. The stability of the class is studied through tools of complex dynamics. Furthermore, we calculate critical and fixed points associated with the rational operator linked to this iterative family. To visualize our findings, we draw dynamical and parameter planes. Hence, we can select the regions where the corresponding method is more efficient or shows chaotic behavior. The conclusions obtained from this stability analysis are used in the numerical section, where the problem of fractional conversion in a chemical reactor and some physical and academic problems are solved. To validate our theoretical findings, we include comparisons with existing methods.