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Theory and Modern Applications

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)