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

Table 1

Maximum absolute error for 𝑁=10,20,30 for Example 4.1.

𝑁	𝛼	𝛽	𝑏	SJCM	𝑏	SJCM
10	2	1	1	8.54⋅10^−7	4	4.18⋅10^0
	1	1		1.54⋅10^−6		4.14⋅10^0
	0.5	−0.5		8.28⋅10^−8		1.15⋅10^0
	−0.5	0.5		1.18⋅10^−6		2.66⋅10^−1
20	2	1	1	8.32⋅10^−16	4	7.52⋅10^−8
	1	1		9.15⋅10^−16		1.33⋅10^−7
	0.5	−0.5		8.04⋅10^−16		2.30⋅10^−9
	−0.5	0.5		3.92⋅10^−16		6.51⋅10^−8
30	2	1	1	6.10⋅10^−16	4	1.18⋅10^−13
	1	1		1.94⋅10^−16		2.14⋅10^−13
	0.5	−0.5		3.33⋅10^−16		7.63⋅10^−14
	−0.5	0.5		3.73⋅10^−16		2.57⋅10^−13