Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

Table 4: Comparison of the proposed new half-step method with Adeyeye & Omar (2018) x-values Error in case one of our method Error in case two our method Error in Adeyeye & Omar (2018) 0.1 1.70091e-15 4.54792e-15 6.34270e-13 0.2 1.91790e-14 3.06193e-14 2.32882e-12 0.3 7.25153e-14 9.80503e-14 5.44348e-12 0.4 1.83912e-13 2.28761-13 9.85317e-12 0.5 3.77884e-13 4.46995e-13 1.59974e-11 0.6 6.81541e-13 7.79496e-13 2.37223e-11 0.7 1.12480e-12 1.25594e-12 3.35679e-11 0.8 1.74091e-12 1.90890e-12 4.53443e-11 0.9 2.56633e-12 2.77460e-12 5.97084e-11 1.0 3.64152e-12 3.89290e-12 7.64322e-11 IV. C onclusions It is evident from the above tables that our proposed new half-step third derivative hybrid block methods are converging faster than the existing method and can handle stiff problems. Comparing the new method with the existing method respectively shows that the new half-step third derivative hybrid block method performs better on stiff and highly stiff problems than the existing method which is of high Order as compared to ours which is of Order four. R eferences R éférences R eferencias 1. Adeyeye O, Omar Z (2018): New Self Starting Approach for Solving Special Third Order Initial Value Problems. International Journal of Pure and Applied Mathematics Vol 118 No. 3, 511-517. 2. Adesanya AO, Fasansi MK, Odekunle MR (2013): One Step Three Hybrid Block Predictor-Corrector Method for the solution of ( ) '' ,' , , ''' y yyxf y = Applied and computational Mathematics Vol 2 (4)137. doi:10.4172/21689679.1000137. 3. Adebayo OA, Adebola EO (2016): One Step Hybrid Method for the Numerical Solution of General Third Order Ordinary Differential Equations. International Journal of Mathematical Sciences, Vol. 2, 5, 1-12. 4. Adoghe LO, Omole EO (2019): A Fifth-Fourth Continuous Block Implicit Hybrid Method for the Solution of Third Order Initial Value Problems in Ordinary Differential Equations. Applied and Computational Mathematics, Vol. 8(3), 50-57. 5. Kuboye JO, Omar Z (2015): Numerical solution of Third Order Ordinary Differential Equations Using a Seven-Step Block Method . International Journal of Mathematical Analysis Vol.9.No.15,743-754. 6. Olabode BT, Momoh AL (2016): Continuous Hybrid Multistep Methods with Legendre Basis Function for Direct Treatment of Second Order Stiff ODEs American Journal of Computational and Applied Mathematics 2016, 6(2): 38-49 DOI: 10.5923/ j.ajcam.20160602.03. 7. Kayode SJ, Obuarhua FO (2013): Continuous y-function Hybrid Methods for Direct Solution of Differential Equations, International Journal of Differential Equations and Application12, 37-48. Half-Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of order Four for the Solution of Third order Ordinary Differential Equations 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 65 ( F ) © 2021 Global Journals Version I N otes