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

Table 4

Errors for the Lax-Wendroff scheme for ℎ=0.02.

𝑘	𝐸num	max|𝑢𝑒−𝑢𝑐|	Error at (0.5, 1.0)	Diss. error	Disp. error
0.001	8.2049×10^−4	0.0026	6.3090×10^−4	1.0506×10^−7	1.1375×10^−6
0.002	6.6803×10^−4	0.0021	5.1728×10^−4	7.1763×10^−8	7.5203×10^−7
1/333	5.1018×10^−4	0.0016	4.0089×10^−4	4.3376×10^−8	4.3728×10^−7
0.004	3.4840×10^−4	0.0011	2.8318×10^−4	2.1247×10^−8	2.0307×10^−7
0.005	1.8166×10^−4	5.8157×10^−4	1.6348×10^−4	6.3582×10^−9	5.4502×10^−8
1/164	1.3952×10^−5	4.3926×10^−5	3.0697×10^−5	1.1388×10^−11	3.6197×10^−10
1/143	1.6764×10^−4	5.3721×10^−4	−7.8352×10^−5	3.8582×10^−9	4.7968×10^−8
1/125	3.5162×10^−4	0.0011	−2.0134×10^−4	1.9362×10^−8	2.0827×10^−7
1/111	5.4133×10^−4	0.0017	−3.2451×10^−4	4.8426×10^−8	4.9113×10^−7
0.01	0.0011	0.0035	−6.5674×10^−4	2.1234×10^−7	1.9665×10^−6