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

Table 2: Comparison of the proposed new half-step method with Mohammed & Adeniyi 2014 x-values Error in case one of our method Error in case two our method Error in Mohammed & Adeniyi 2014 0.1 1.0434e-14 4.1832e-15 1.0000e-10 0.2 9.8731e-14 1.8599e-14 3.0000e-10 0.3 3.1317e-13 4.4245e-14 7.0000e-10 0.4 6.6668e-13 8.0431e-14 7.0000e-10 0.5 1.1507e-12 1.2552e-13 6.0000e-10 0.6 1.7445e-12 1.7743e-13 2.0000e-10 0.7 2.4220e-12 2.3395 e-13 9.0000e-10 0.8 3.1554e-12 2.9298e-13 2.8000e-09 0.9 3.9178e-12 3.5259e-13 5.4000e-09 1.0 4.6852e-12 4.1112e-13 3.5000e-09 Problem III: We consider the third order ODE 10'' ,0 0' ,10 , '4 ''' = = = + −=                         y y yxy y Exact Solution: 10 1 , 8 2 2 cos 1 16 3 = + − =               h x x xy Table 3: Comparison of the proposed new half-step method with Adebayo & Adebola (2016) x-values Error in case one of our method Error in case two our method Error in Adebayo &Adebola (2016) 0.1 7.9512e-14 3.1484e-14 2.970e-08 0.2 8.6717e-13 1.5843e-13 1.988e-07 0.3 3.1385e-12 4.2379e-13 6.508e-07 0.4 7.5504e-12 8.5820e-13 1.5480e-06 0.5 1.4585e-11 1.4765e-12 3.062e-06 0.6 2.4504e-11 2.2752e-12 5.3625e-06 0.7 3.7317e-11 3.2313e-12 8.6068e-06 0.8 5.2765e-11 4.3022e-12 1.2926e-05 0.9 7.0321e-11 5.4266e-12 1.8118e-05 1.0 8.9206e-11 6.5277e-12 2.5129e-05 Problem IV: .1 0,50'' ,10' ,30 , exp ''' ≤≤ = = = =                               x y y y x y Exact Solution: 10 1 222 = + +=       h with xe x xy Half-Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of order Four for the Solution of Third order Ordinary Differential Equations © 2021 Global Journals 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 64 ( F ) Version I N otes