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