Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Example 4: The maximum absolute errors

From: A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasi-linear hyperbolic equations

h	$O (k^{2} + h^{4})$ -method			$O (k^{2} + h^{4})$ -method
h	$γ = 1$	$γ = 5$	$γ = 10$	$γ = 1$	$γ = 5$	$γ = 10$
$\frac{1}{8}$	0.5927(-05)	0.6006(-04)	0.5058(-03)	0.3267(-03)	0.2746(-02)	0.4598(-01)
$\frac{1}{16}$	0.3601(-06)	0.3476(-05)	0.3100(-04)	0.6032(-04)	0.3570(-03)	0.4750(-02)
$\frac{1}{32}$	0.2225(-07)	0.2150(-06)	0.1952(-05)	0.1398(-04)	0.6526(-04)	0.8192(-03)
$\frac{1}{64}$	0.1389(-08)	0.1339(-07)	0.1222(-06)	0.3438(-05)	0.1515(-04)	0.1713(-03)

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