A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

Table 1

Comparison of the LB finite difference solutions with exact solution at 𝑇=0.1 for 𝜈=1 with 𝜏=1.

𝑥	Numerical solution			Exact solution
	𝑁=10	𝑁=20	𝑁=100
0.1	0.00847	0.01059	0.01129	0.01132
0.2	0.01370	0.01715	0.01828	0.01833
0.3	0.01371	0.01716	0.01830	0.01835
0.4	0.00848	0.01061	0.01132	0.01135
0.5	0.00000	0.00000	0.00000	0.00000
0.6	−0.00848	−0.01061	−0.01132	−0.01135
0.7	−0.01371	−0.01716	−0.01830	−0.01835
0.8	−0.01370	−0.01715	−0.01829	−0.01833
0.9	−0.00847	−0.01059	−0.01129	−0.01132