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

Table 5

Errors for NSFD scheme for ℎ=0.02.

𝑘	𝐸num	max|𝑢𝑒−𝑢𝑐|	Error at (0.5, 1.0)	Diss. error	Disp. error
0.001	0.0035	0.0100	0.0100	1.2802×10^−5	8.0987×10^−6
0.002	0.0028	0.0083	0.0083	8.6039×10^−6	5.5211×10^−6
1/333	0.0022	0.0064	0.0064	5.1527×10^−6	3.3593×10^−6
0.004	0.0015	0.0045	0.0045	2.5390×10^−6	1.6870×10^−6
0.005	8.7288×10^−4	0.0026	0.0026	8.0435×10^−7	5.5063×10^−7
1/164	1.1717×10^−4	3.5591×10^−4	3.4999×10^−4	1.2220×10^−8	1.2981×10^−8
1/143	5.2775×10^−4	0.0016	−0.0015	3.0107×10^−7	1.9762×10^−7
1/125	0.00126	0.0038	−0.0037	1.7163×10^−6	1.1639×10^−6
1/111	0.0020	0.0061	−0.0060	4.3904×10^−6	3.0429×10^−6
0.01	0.0028	0.0085	−0.0084	8.3500×10^−6	5.8963×10^−6