Mathematical Problems in Engineering

Research Article

New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method

Table 2

Maximum absolute error for 𝑁 = 8 , 1 6 , 2 8 , 3 2 , 4 0 for Example 4.2.
𝑁 𝛼 𝛽 𝑏 SJCM 𝑏 SJCM
8 0.5 0.5 1 2 . 9 6 ⋅ 1 0 − 5 4 1 . 4 5 ⋅ 1 0 − 1
0 0 3 . 3 8 ⋅ 1 0 − 7 1 . 8 9 ⋅ 1 0 − 2
−0.5 −0.5 1 . 4 7 ⋅ 1 0 − 5 8 . 2 4 ⋅ 1 0 − 2
16 0.5 0.5 1 4 . 0 6 ⋅ 1 0 − 1 1 4 1 . 0 1 ⋅ 1 0 − 4
0 0 9 . 0 5 ⋅ 1 0 − 1 4 8 . 9 5 ⋅ 1 0 − 8
−0.5 −0.5 6 . 6 3 ⋅ 1 0 − 1 2 2 . 0 4 ⋅ 1 0 − 5
24 0.5 0.5 1 2 . 2 4 ⋅ 1 0 − 1 6 4 6 . 5 0 ⋅ 1 0 − 8
0 0 3 . 3 3 ⋅ 1 0 − 1 6 2 . 3 7 ⋅ 1 0 − 1 1
−0.5 −0.5 4 . 4 4 ⋅ 1 0 − 1 6 7 . 6 2 ⋅ 1 0 − 9
32 0.5 0.5 1 3 . 3 3 ⋅ 1 0 − 1 6 4 3 . 8 3 ⋅ 1 0 − 1 1
0 0 4 . 4 4 ⋅ 1 0 − 1 6 8 . 8 8 ⋅ 1 0 − 1 5
−0.5 −0.5 4 . 4 4 ⋅ 1 0 − 1 6 3 . 1 9 ⋅ 1 0 − 1 2
40 0.5 0.5 1 3 . 3 3 ⋅ 1 0 − 1 6 4 1 . 7 3 ⋅ 1 0 − 1 4
0 0 4 . 4 4 ⋅ 1 0 − 1 6 8 . 6 5 ⋅ 1 0 − 1 5
−0.5 −0.5 4 . 4 4 ⋅ 1 0 − 1 6 2 . 4 4 ⋅ 1 0 − 1 5