Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 23 Issue 4

V. C onvergence and C onsistency A nalysis Test of convergence: The iteration method will be convergent if the set of solutions (or frequencies Ω or amplitudes T k ) in ascending order satisfy the following property. = Lim( ) or, Ω = Lim(Ω ) or, T = Lim(T ) , k → ∞ Here is considered as the exact solution, Ω denotes the frequencies and T k denotes the corresponding periods of the nonlinear oscillator. In the obtained solutions, it has been indicated that there is less error to iterative steps in ascending order and finally it has been shown that | 2 − | < , where ε is a small positive number. Hence the presented extended iteration method is convergent. Test of consistency: The iterative method will be consistent if the set of solutions (or frequencies Ω or amplitudes T k ) in ascending order satisfy the following property Lim| − | = 0 or, Lim|Ω − Ω | = 0 or, Lim| − | = 0 , → ∞ In the obtained solutions, it has been indicated that there is less error to iterative steps in ascending order, and finally, it has been shown that, Lim| − | = 0 , → ∞ as | 2 − | = 0 . Hence the presented extended iteration method is consistent. VI. C onclusion In this research, it has been seen that the most significant part of solutions has been enhanced drastically. The modified solutions show that this modification is more Figure 2: Approximate solutions of ⃛ +̇ = ̇̈ for = 0.1 Compare with the corresponding numerical solution. © 2023 Global Journals 1 Year 2023 56 Global Journal of Science Frontier Research Volume XXIII Issue ersion I V ( F ) By an Extended Iteration Method to Adequate Solutions of Jerk Oscillator Containing Displacement Times Velocity Time’s Acceleration and Velocity N otes IV