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Theory and Modern Applications

Table 5 Problem 6.4 : 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  = 2

γ  = 20

γ  = 2

γ  = 20

1/8

2.2955(−04)

1.8526(−03)

7.4446(−04)

5.2318(−03)

1/16

1.3364(−05)

1.0955(−04)

5.7172(−05)

3.3478(−04)

1/32

8.2180(−07)

6.9282(−06)

3.6105(−06)

2.1633(−05)

1/64

4.9859(−08)

4.4854(−07)

2.3129(−07)

1.4261(−06)