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Theory and Modern Applications

Table 6 Problem 6.5 : 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 ( 4.25 )

Method discussed in [ 28 ]

α  = 0.5

α  = 0.05

α  = 0.5

α  = 0.05

1/8

2.7548(−04)

2.7548(−04)

9.2520(−04)

9.2520(−04)

1/16

1.7425(−05)

1.7424(−05)

6.1778(−05)

6.1776(−05)

1/32

1.0947(−06)

1.0924(−06)

3.9018(−06)

3.8992(−06)

1/64

7.1330(−08)

6.8337(−08)

2.5636(−07)

2.4124(−07)