New Iterative Method (NIM): a semi-analytic solution for Rössler system

• Main Author: Chowdhury, Md. Sazzad Hossien
• Format: Conference or Workshop Item
• Language: English; English
• Published: 2021
• Subjects: QA Mathematics; QA297 Numerical Analysis
• Online Access: http://irep.iium.edu.my/94007/8/94007_New%20Iterative%20Method%20_text%282%29.pdf; http://irep.iium.edu.my/94007/9/94007_New%20Iterative%20Method%20_text%283%29.pdf; http://irep.iium.edu.my/94007/

This paper draws special attention to the strength of New Iterative Method (NIM) in numerically solving the Rössler system. The Rössler system is a system of nonlinear ordinary differential equations (ODEs) with chaotic and non-chaotic behaviours. The proposed method finds solutions for the differential equations with the conditions of the Rössler system via the Banach contraction principle. The presented technique gives excellent results as compared with the corresponding numerical results of Runge–Kutta method (RK4) in the tabular as well as graphical form. The RK4 method cannot provide explicit series solution. Whereas NIM procedure can come up with explicit series solution as well as numerical solutions to the benchmark problem. which reveal that the proposed analytical approximation technique is novel and reliable for other non-linear problems as well.