Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

Table 3

Representation of the error by increasing the number of terms in our polynomial solution.

(a)

	𝑁=10	𝑁=12	𝑁=14
(𝛼,𝛽)=(0,0)	1.02×10^−9	2.13×10^−10	2.65×10^−12
(𝛼,𝛽)=(−0.4,−0.4)	2.26×10^−10	3.23×10^−11	2.12×10^−13
(𝛼,𝛽)=(−0.5,−0.5)	2.33×10^−10	1.18×10^−10	1.05×10^−13
(𝛼,𝛽)=(−0.4,0.6)	7.16×10^−10	1.01×10^−10	3.55×10^−12
(𝛼,𝛽)=(0.6,0.6)	6.37×10^−8	2.24×10^−9	3.70×10^−11
(𝛼,𝛽)=(2,2)	4.25×10^−6	1.66×10^−7	2.39×10^−9

(b)

	𝑁=16	𝑁=18	𝑁=20
(𝛼,𝛽)=(0,0)	1.31×10^−15	1.21×10^−18	2.09×10^−22
(𝛼,𝛽)=(−0.4,−0.4)	4.23×10^−16	7.45×10^−19	9.76×10^−22
(𝛼,𝛽)=(−0.5,−0.5)	1.62×10^−15	3.28×10^−20	1.12×10^−23
(𝛼,𝛽)=(−0.4,0.6)	5.60×10^−14	4.08×10^−19	5.35×10^−22
(𝛼,𝛽)=(0.6,0.6)	2.36×10^−13	1.85×10^−17	3.19×10^−20
(𝛼,𝛽)=(2,2)	4.17×10^−11	3.06×10^−13	7.11×10^−16