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Theory and Modern Applications

Table 13 Example  4 : Case 4.4: Maximum absolute errors \(\pmb{\alpha = 1}\) , \(\pmb{\beta = 0}\)

From: High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations

N  + 1

Proposed method ( 3.6 )

Method given in [ 4 ]

\(\boldsymbol {R_{e} = 10^{2\vphantom{\sum^{i}}}}\)

\(\boldsymbol {R_{e} = 10^{4}}\)

\(\boldsymbol {R_{e} = 10^{6}}\)

\(\boldsymbol {R_{e} = 10^{2}}\)

\(\boldsymbol {R_{e} = 10^{4}}\)

\(\boldsymbol {R_{e} = 10^{6}}\)

8

8.8258(–06)

1.9258(–09)

1.0430(–13)

4.1061(–04)

8.3710(–08)

8.4373(–12)

16

4.9239(–07)

9.7076(–11)

1.0463(–14)

1.1067(–04)

2.2489(–08)

2.2700(–12)

32

4.2004(–08)

7.3269(–12)

9.9642(–16)

2.7680(–05)

5.7437(–09)

5.7920(–13)

64

1.0396(–08)

1.2489(–12)

1.3421(–16)

6.9473(–06)

1.4564(–09)

1.4698(–13)