Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Temporal convergence rates for Example 4.2 with fixed spatial resolution \(J_{x}=400\)

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

h	σ = 100, ν = 0.1
	EAC3					AB3
	\(E_{\infty }(t)\)	\(\mathit{rate}_{t}\)	\(E_{R2}(t)\)	\(\mathit{rate}_{t}\)	cpu	\(E_{\infty }(t)\)	\(\mathit{rate}_{t}\)	\(E_{R2}(t)\)	\(\mathit{rate}_{t}\)	cpu
2⁻³	8.74 × 10⁻⁷	–	3.71 × 10⁻⁴	–	0.07	8.70 × 10⁻⁷	–	3.71 × 10⁻⁴	–	0.14
2⁻⁴	1.24 × 10⁻⁷	2.82	5.26 × 10⁻⁵	2.82	0.17	1.23 × 10⁻⁷	2.82	5.25 × 10⁻⁵	2.82	0.31
2⁻⁵	1.62 × 10⁻⁸	2.93	6.91 × 10⁻⁶	2.93	0.34	1.61 × 10⁻⁸	2.93	6.89 × 10⁻⁶	2.93	0.65
2⁻⁶	2.08 × 10⁻⁹	2.97	8.84 × 10⁻⁷	2.97	0.74	2.06 × 10⁻⁹	2.97	8.78 × 10⁻⁷	2.97	1.20
2⁻⁷	2.62 × 10⁻¹⁰	2.98	1.12 × 10⁻⁷	2.98	1.38	2.64 × 10⁻¹⁰	2.97	1.11 × 10⁻⁷	2.99	2.38

h	EAC4					AM4
h	\(E_{\infty }(t)\)	\(\mathit{rate}_{t}\)	\(E_{R2}(t)\)	\(\mathit{rate}_{t}\)	cpu	\(E_{\infty }(t)\)	\(\mathit{rate}_{t}\)	\(E_{R2}(t)\)	\(\mathit{rate}_{t}\)	cpu
2⁻³	7.14 × 10⁻⁷	–	3.03 × 10⁻⁴	–	0.08	7.09 × 10⁻⁷	–	3.03 × 10⁻⁴	–	0.15
2⁻⁴	1.14 × 10⁻⁷	2.64	4.87 × 10⁻⁵	2.64	0.17	1.14 × 10⁻⁷	2.63	4.87 × 10⁻⁵	2.64	0.38
2⁻⁵	1.57 × 10⁻⁸	2.87	6.67 × 10⁻⁶	2.87	0.34	1.61 × 10⁻⁸	2.83	6.80 × 10⁻⁶	2.84	0.87
2⁻⁶	2.04 × 10⁻⁹	2.94	8.69 × 10⁻⁷	2.94	0.76	2.33 × 10⁻⁹	2.79	9.64 × 10⁻⁷	2.82	1.75
2⁻⁷	2.60 × 10⁻¹⁰	2.97	1.11 × 10⁻⁷	2.97	1.45	4.72 × 10⁻¹⁰	2.30	2.04 × 10⁻⁷	2.24	3.72

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