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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 The MAEs for Example 4 at \(\pmb{t=1.0}\) for a fixed \(\pmb{\lambda =(k/h^{2})=1.6}\) (uniform 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

h

 

\(\boldsymbol {O(k^{2}+ h^{4})}\) -method ( 28a )-( 28b )

\(\boldsymbol {O(k^{2}+ h^{2})}\) -method ( 27a )-( 27b )

 

ϵ  = 0.1

ϵ  = 0.01

ϵ  = 0.001

ϵ  = 0.1

ϵ  = 0.01

ϵ  = 0.001

1/8

u

3.0988 (−04)

2.9825 (−05)

3.5010 (−06)

3.2430 (−02)

1.0781 (−02)

1.1932 (−03)

\(u_{xx}\)

2.4409 (−03)

3.8680 (−04)

4.4212 (−05)

3.9514 (−01)

1.1690 (−01)

1.2865 (−02)

1/16

u

1.9387 (−05)

1.8905 (−06)

2.2211 (−07)

8.0703 (−03)

2.7648 (−03)

3.0660 (−04)

\(u_{xx}\)

1.5294 (−04)

2.4412 (−05)

2.7933 (−06)

9.9261 (−02)

3.0176 (−02)

3.3273 (−03)

1/32

u

1.2121 (−06)

1.1856 (−07)

1.3934 (−08)

2.0148 (−03)

6.9554 (−04)

7.7174 (−05)

\(u_{xx}\)

9.5655 (−06)

1.5293 (−06)

1.7506 (−07)

2.4840 (−02)

7.6039 (−03)

8.3890 (−04)

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