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

e) Numerical Example Problem I We consider a highly stiff problem ,1 0'' ,00' ,10 ,0 ' '' ''' −= = = =−+−                         y y y yy y y Exact Solution: 100 1 , cos = =       hx xy Table 1: Comparison of the proposed new half-step method with Adoghe & Omole (2019) x-values Error in case one of our method Error in case two our method Error in Adoghe & Omole 2019 0.01 6.100e-20 3.0000e-20 0.0000e+00 0.02 1.200e-19 6.0000e-20 1.1102e-16 0.03 1.900e-19 1.2000e-19 4.4409e-16 0.04 2.500e-19 1.6000e-19 5.8842e-15 0.05 3.200e-19 1.9000e-19 2.6201e-14 0.06 3.900e-19 2.5000e-19 8.3822e-14 0.07 4.500e-19 2.8000e-19 2.0750e-13 0.08 5.100e-19 3.2000e-19 4.4142e-13 0.09 5.600e-19 3.5000e-19 8.4743e-13 0.10 6.300e-19 4.0000e-19 1.5086e-12 Problem II We consider a highly stiff problem ,1 0'' ,00' ,10 ,0 3'7''5''' −= = = = + + +                         y y y y y y y Exact Solution: 10 1 , = − + − =       h x ex x e xy 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 63 ( F ) © 2021 Global Journals Version I N otes