Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations

Table 4

Convergence rates at 𝑡=1 with 𝜇=0.1, 𝛼=1, 𝛽=0.01, 𝛾=3, and 𝑛=2.

𝑁	𝜏	𝐿∞-error	Order	𝐿2-error	Order
4	2𝐸−5	2.986𝐸−01	—	4.722𝐸−01	—
8		2.064𝐸−03	𝑁^−7.18	1.403𝐸−03	𝑁^−8.39
12		5.166𝐸−06	𝑁^−14.77	2.429𝐸−06	𝑁^−15.68
16		5.213𝐸−09	𝑁^−23.98	1.899𝐸−09	𝑁^−24.88
20		2.750𝐸−10	𝑁^−13.19	7.859𝐸−11	𝑁^−14.27
36	2∗10^−3	2.734𝐸−06	—	4.368𝐸−07	—
	1∗10^−3	6.836𝐸−07	𝜏^2.00	1.092𝐸−07	𝜏^2.00
	2∗10^−4	2.734𝐸−08	𝜏^2.00	4.368𝐸−09	𝜏^2.00
	1∗10^−4	6.836𝐸−09	𝜏^2.00	1.092𝐸−09	𝜏^2.00
	2∗10^−5	2.733𝐸−10	𝜏^2.00	4.366𝐸−11	𝜏^2.00