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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
γ = 1 γ = 5 γ = 10 γ = 1 γ = 5 γ = 10
1 8 0.5927(-05) 0.6006(-04) 0.5058(-03) 0.3267(-03) 0.2746(-02) 0.4598(-01)
1 16 0.3601(-06) 0.3476(-05) 0.3100(-04) 0.6032(-04) 0.3570(-03) 0.4750(-02)
1 32 0.2225(-07) 0.2150(-06) 0.1952(-05) 0.1398(-04) 0.6526(-04) 0.8192(-03)
1 64 0.1389(-08) 0.1339(-07) 0.1222(-06) 0.3438(-05) 0.1515(-04) 0.1713(-03)