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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 15 Example  7 : Maximum absolute errors, \(\pmb{\varepsilon = 1}\) , \(\pmb{\alpha_{1} = \beta_{1} = - 2}\) , \(\pmb{\alpha_{2} = \beta_{2} = 1}\) , \(\pmb{\lambda = 1.6/4\pi^{2}}\)

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 ]

t  = 1.0

t  = 2.0

t  = 1.0

t  = 2.0

8

u

5.7826(–04)

4.2579(–05)

7.4756(–04)

6.1386(–04)

v

5.7826(–04)

4.2579(–05)

7.4756(–04)

6.1386(–04)

16

u

3.5478(–05)

2.6105(–07)

5.1124(–05)

3.8618(–05)

v

3.5478(–05)

2.6105(–07)

5.1124(–05)

3.8618(–05)

32

u

2.2070(–06)

1.6238(–06)

3.3516(–06)

2.4173(–06)

v

2.2070(–06)

1.6238(–06)

3.3516(–06)

2.4173(–06)

64

u

1.3777(–07)

1.0137(–07)

2.2035(–07)

1.5114(–07)

v

1.3777(–07)

1.0137(–07)

2.2035(–07)

1.5114(–07)

128

u

8.6048(–09)

6.3339(–09)

1.3837(–08)

9.3878(–09)

v

8.6048(–09)

6.3339(–09)

1.3837(–08)

9.3878(–09)

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