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Theory and Modern Applications

Table 1 Example 1 : the maximum absolute errors

From: A new variable mesh method based on non-polynomial spline in compression approximations for 1D quasilinear hyperbolic equations

N  + 1

Proposed method ( 5.11 )

Results given in [ 23 ]

γ  = 1

γ  = 2

γ  = 1

γ  = 2

8

0.5448(−02)

0.8876(−02)

0.6100(−02)

0.1200(−01)

16

0.1126(−02)

0.2216(−02)

0.1600(−02)

0.3600(−02)

32

0.4848(−03)

0.8672(−03)

0.6162(−03)

0.1200(−02)

64

0.2088(−03)

0.3474(−03)

0.2643(−03)

0.5281(−03)