Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Example 3: 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	$γ = 1$	$γ = 5$	$γ = 10$	$γ = 1$	$γ = 5$	$γ = 10$
$\frac{1}{8}$	0.1015(−03)	0.1831(−02)	0.4422(−01)	0.3267(−03)	0.2746(−02)	0.4598(−01)
$\frac{1}{16}$	0.6438(−05)	0.1080(−03)	0.3198(−02)	0.6032(−04)	0.3570(−03)	0.4750(−02)
$\frac{1}{32}$	0.4032(−06)	0.6806(−05)	0.1840(−03)	0.1398(−04)	0.6526(−04)	0.8192(−03)
$\frac{1}{64}$	0.2194(−07)	0.4252(−06)	0.1126(−04)	0.3438(−05)	0.1515(−04)	0.1713(−03)

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