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Theory and Modern Applications

Table 8 The MAEs for Example 8 at \(\pmb{t=1.0, \eta=0.92}\) (quasi-variable mesh)

From: A class of quasi-variable mesh methods based on off-step discretization for the numerical solution of fourth-order quasi-linear parabolic partial differential equations

N  + 1

 

\(\boldsymbol {O(k^{2}+ k^{2}h_{l}+h_{l}^{3})}\) -method ( 16a )-( 16b )

\(\boldsymbol {O(k^{2}+ h_{l}^{2})}\) -method ( 15a )-( 15b )

 

α  = 10

α  = 20

α  = 40

α  = 10

α  = 20

α  = 40

8

u

3.3667 (−05)

7.7683 (−05)

1.7212 (−02)

2.6072 (−04)

3.0874 (−04)

2.6133 (−02)

\(u_{xx}\)

3.3298 (−04)

7.6915 (−04)

1.7290 (−01)

2.3571 (−04)

7.0446 (−04)

2.5645 (−01)

16

u

2.1139 (−06)

4.7259 (−06)

1.0805 (−03)

8.6976 (−05)

1.0909 (−04)

9.5763 (−03)

\(u_{xx}\)

2.1334 (−05)

4.7049 (−05)

1.0817 (−02)

1.2171 (−04)

3.4424 (−04)

9.4655 (−02)

32

u

1.3319 (−07)

2.7901 (−07)

7.8958 (−05)

4.1496 (−05)

5.1293 (−05)

3.9491 (−03)

\(u_{xx}\)

1.5345 (−06)

2.9686 (−06)

7.9178 (−04)

5.4398 (−05)

1.5469 (−04)

3.9160 (−02)