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

Table 2: Approximate periods obtained by our method compared with exact periods and other existing periods of xxx x x    =+ : A exact T Modified ( ) Er(%) Gottlieb Er(%) (2004) [6] Ma et al. Er(%) (2008) [15] Ramos (2010) [21] Er(%) Karahan (2017) [14] Er(%) Gamal (2021) [13] Er(%) 0.1 6.275347 6.275347 2.60 e -6 6.275346 1.3 e -5 6.275347 2.5 e -6 6.275329 7.2 e -5 6.275347 3.19 e -6 6.275334 2.11 e -4 0.2 6.252016 6.252016 9.53 e -8 6.252003 2.11 e -4 6.252016 1.6 e -7 6.251740 1.1 e -3 6.252016 3.20 e -6 6.252016 1.59 e -7 0.5 6.096061 6.096062 1.18 e -5 6.095585 7.08 e -3 6.096059 3.21 e -5 6.085649 4.6 e -2 6.275334 2.94 6.275334 3.28 e -5 1 5.626007 5.625880 2.26 e -3 5.619852 1.09 e -1 5.625795 3.8 e -3 5.477174 9.0 e -1 5.624549 2.60 e -2 6.275334 2.31 e -4 2 4.491214 4.614498 2.74 4.442883 1.08 4.482081 2.03 4.466205 5.6 e -1 4.466455 5.51 e -1 4.47661 3.25 e -1 Approximate period obtained by Gottlieb, Ma et al. Ramos, Karahan, and Ismail, respectively denoted by , , , , and the modified second approximate periodreceived by us is represented by 2 . Percentage error is indicated by Er(%). e 2: Figure 1: Approximate solutions of ⃛ +̇ = ̇ ̈ for = 0.5 Compare with the corresponding numerical solution. 1 Year 2023 55 Frontier Research Volume XXIII Issue ersion I V ( F ) Science © 2023 Global Journals Global Journal of By an Extended Iteration Method to Adequate Solutions of Jerk Oscillator Containing Displacement Times Velocity Time’s Acceleration and Velocity N otes IV