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

Table 2

Errors for Crank-Nicolson scheme.

𝑘	ℎ	cfl	𝐸num	max|𝑢𝑒−𝑢𝑐|	Error at (0.5, 1.0)	Diss. error	Disp. error
0.005	0.02	0.25	9.9859×10^−4	0.0032	7.3954×10^−4	1.4704×10^−7	1.6929×10^−6
0.01	0.02	0.50	0.0011	0.0035	7.3475×10^−4	1.6161×10^−7	2.0307×10^−6
0.02	0.02	1.0	0.0015	0.0046	7.4486×10^−4	2.2664×10^−7	3.7049×10^−6
0.04	0.02	2.0	0.0029	0.0092	0.0013	5.9447×10^−7	1.5389×10^−5
0.005	0.04	0.125	0.0037	0.0114	0.0020	2.2440×10^−6	2.3758×10^−5
0.01	0.04	0.25	0.0038	0.0116	0.0020	2.2981×10^−6	2.4852×10^−5
0.02	0.04	0.5	0.0042	0.0126	0.0021	2.5212×10^−6	2.9471×10^−5
0.04	0.04	1.0	0.0055	0.0162	0.0028	3.5178×10^−6	5.1581×10^−5