Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes

Table 1

Errors for Lax-Wendroff scheme.

𝑘	ℎ	cfl	𝐸num	max|𝑢𝑒−𝑢𝑐|	Error at (0.5, 1.0)	Diss. error	Disp. error
0.005	0.02	0.25	1.8166×10^−4	5.8157×10^−4	1.6348×10^−4	6.3582×10^−9	5.4502×10^−8
0.01	0.02	0.50	7.3296×10^−4	0.0024	1.6348×10^−4	9.1960×10^−8	8.9741×10^−7
0.01	0.04	0.25	0.0021	0.0065	0.0011	9.1500×10^−7	7.1622×10^−6
0.02	0.04	0.50	1.2252×10^−4	3.7946×10^−4	3.7946×10^−4	4.0896×10^−9	2.4477×10^−8