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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 16 Example  8 : Maximum absolute errors at \(\pmb{t = 1}\) , \(\pmb{\alpha_{1} = \beta_{1} = 2}\) , \(\pmb{\alpha_{2} = \beta_{2} = - 1}\) , \(\pmb{\lambda = 3.2}\)

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 ( 4.28 )

Method given in [ 10 ]

\(\boldsymbol {R_{e} = 100}\)

\(\boldsymbol {R_{e} = 200}\)

\(\boldsymbol {R_{e} = 250}\)

\(\boldsymbol {R_{e} = 100}\)

\(\boldsymbol {R_{e} = 200}\)

\(\boldsymbol {R_{e} = 250}\)

8

u

6.3075(–06)

3.9152(–06)

3.2823(–06)

8.0563(–06)

4.3982(–06)

3.5838(–06)

v

6.3075(–06)

3.9152 (–06)

3.2837(–06)

8.0563(–06)

4.3982(–06)

3.5838(–06)

16

u

4.1145(–07)

2.4266(–07)

2.0268(–07)

5.0129(–07)

2.8249(–07)

2.2612(–07)

v

4.1145(–05)

2.4266(–07)

2.0268(–07)

5.0129(–07)

2.8249(–07)

2.2612(–07)

32

u

2.5696(–08)

1.5236(–08)

1.2647(–08)

3.1617(–08)

1.7629(–08)

1.4379(–08)

v

2.5696(–08)

1.5236(–08)

1.2647(–08)

3.1617(–08)

1.7629(–08)

1.4379(–08)

64

u

1.6133(–09)

9.5490(–10)

7.9187(–10)

1.9755(–09)

1.1015(–09)

8.9877(–10)

v

1.6133(–09)

9.5490(–10)

7.9187(–10)

1.9755(–09)

1.1015(–09)

8.9877(–10)

128

u

1.0082(–10)

5.9683(–11)

4.9531(–11)

1.2337(–10)

6.8803(–11)

5.6159(–11)

v

1.0082(–10)

5.9683(–11)

4.9531(–11)

1.2337(–10)

6.8803(–11)

5.6159(–11)

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