Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Numerical results of one-dimensional parabolic problem at \(t=0.1\) for case 2 of Example 1

From: A new high-order compact finite difference scheme based on precise integration method for the numerical simulation of parabolic equations

		N
		11	21	41	81
Taylor	Max(error)	5.485 × 10⁻⁴	6.897 × 10⁻⁶	9.124 × 10⁻⁹	3.565 × 10⁻¹¹
	CPU (s)	0.023	0.022	0.024	0.025
	Order	–	6.313	9.562	8.000
Padé	Max(error)	5.485 × 10⁻⁴	6.896 × 10⁻⁶	8.956 × 10⁻⁹	3.565 × 10⁻¹¹
	CPU (s)	0.023	0.023	0.026	0.027
	Order	–	6.314	9.589	7.973
RK4	Max(error)	5.485 × 10⁻⁴	6.897 × 10⁻⁶	9.124 × 10⁻⁹	3.532 × 10⁻¹¹
	CPU (s)	0.452	0.510	0.859	3.506
	Order	–	6.314	9.562	8.013

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