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Table 1 Example 1: 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 4 + h 4 )-method discussed in [33]
γ = 1 , t = 5 γ = 2 , t = 5 γ = 1 , t = 5 γ = 2 , t = 5
1 8 0.4559(−04) 0.3865(−04) 0.6486(−04) 0.5784(−04)
1 16 0.2850(−05) 0.2416(−05) 0.4291(−05) 0.3808(−05)
1 32 0.1781(−06) 0.1510(−06) 0.2774(−06) 0.2424(−06)
1 64 0.1113(−07) 0.9442(−08) 0.1612(−07) 0.1566(−07)