Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 6 Comparison of accuracy of three methods for different time steps in Example 4.3

From: Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme

t	u
	EAC3		AB3		AM4
	\(E_{\infty }(t)\)	\(E_{R2}(t)\)	\(E_{\infty }(t)\)	\(E_{R2}(t)\)	\(E_{\infty }(t)\)	\(E_{R2}(t)\)
0.5	2.76 × 10⁻⁷	3.93 × 10⁻⁷	1.91 × 10⁻⁶	2.83 × 10⁻⁶	4.74 × 10⁻³	7.50 × 10⁻³
1.0	2.01 × 10⁻⁷	5.13 × 10⁻⁷	1.40 × 10⁻⁶	3.69 × 10⁻⁶	7.40 × 10⁻³	1.87 × 10⁻²
2.0	6.67 × 10⁻⁸	4.81 × 10⁻⁷	5.45 × 10⁻⁷	4.01 × 10⁻⁶	5.14 × 10⁻³	3.32 × 10⁻²
3.0	1.86 × 10⁻⁸	3.71 × 10⁻⁷	1.97 × 10⁻⁷	3.95 × 10⁻⁶	2.46 × 10⁻³	4.09 × 10⁻²

t	v
	EAC3		AB3		AM4
	\(E_{\infty }(t)\)	\(E_{R2}(t)\)	\(E_{\infty }(t)\)	\(E_{R2}(t)\)	\(E_{\infty }(t)\)	\(E_{R2}(t)\)
0.5	2.89 × 10⁻⁷	4.10 × 10⁻⁷	1.89 × 10⁻⁶	2.82 × 10⁻⁶	4.74 × 10⁻³	7.50 × 10⁻³
1.0	2.14 × 10⁻⁷	5.38 × 10⁻⁷	1.40 × 10⁻⁶	3.70 × 10⁻⁶	7.40 × 10⁻³	1.87 × 10⁻⁶
2.0	7.07 × 10⁻⁸	5.08 × 10⁻⁷	5.48 × 10⁻⁷	4.04 × 10⁻⁶	5.14 × 10⁻³	3.32 × 10⁻²
3.0	1.99 × 10⁻⁸	3.97 × 10⁻⁷	1.98 × 10⁻⁷	3.98 × 10⁻⁶	2.46 × 10⁻³	4.09 × 10⁻²

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