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Theory and Modern Applications

Table 4 Problem 6.3 : The maximum absolute errors

From: A new spline in compression method of order four in space and two in time based on half-step grid points for the solution of the system of 1D quasi-linear hyperbolic partial differential equations

h

Proposed method ( 3.12 )

Method discussed in [ 35 ]

γ  = 0.5

γ  = 2

γ  = 0.5

γ  = 2

1/8

5.0419(−04)

9.3631(−04)

2.1822(−03)

1.5863(−03)

1/16

3.1579(−05)

5.8584(−05)

1.6354(−04)

1.1132(−04)

1/32

1.9734(−06)

3.6602(−06)

1.1177(−05)

7.6658(−06)

1/64

1.2362(−07)

2.2966(−07)

8.6172(−07)

5.8284(−07)