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

Table 5

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	1𝐸−5	1.722𝐸−02	—	2.112𝐸−02	—
8		2.049𝐸−05	𝑁^−9.71	1.437𝐸−05	𝑁^−10.52
12		3.901𝐸−09	𝑁^−21.13	1.845𝐸−09	𝑁^−22.10
16		4.639𝐸−12	𝑁^−23.41	1.963𝐸−12	𝑁^−23.80
20		4.718𝐸−12	—	1.570𝐸−12	—
36	2∗10^−3	2.048𝐸−07	—	3.511𝐸−08	—
	1∗10^−3	5.119𝐸−08	𝜏^2.00	8.777𝐸−09	𝜏^2.00
	2∗10^−4	2.047𝐸−09	𝜏^2.00	3.511𝐸−10	𝜏^2.00
	1∗10^−4	5.117𝐸−10	𝜏^2.00	8.778𝐸−11	𝜏^2.00
	2∗10^−5	2.028𝐸−11	𝜏^2.01	3.535𝐸−12	𝜏^2.00