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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 10 The MAEs for Example 10 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 ( 49a )-( 49b )

\(\boldsymbol {O(k^{2}+ h^{2})}\) -method ( 48a )-( 48b )

 

α  = 1

α  = 10

α  = 20

α  = 1

α  = 10

α  = 20

1/8

u

1.0745 (−05)

1.3706 (−05)

1.9813 (−05)

9.7462 (−03)

1.2495 (−02)

1.7658 (−02)

\(u_{xx}-u_{t}\)

2.4924 (−04)

2.2351 (−04)

1.7245 (−04)

3.9007 (−02)

6.3033 (−02)

1.0975 (−01)

1/16

u

6.6313 (−07)

8.4307 (−07)

1.2147 (−06)

2.4146 (−03)

3.0834 (−03)

4.3337 (−03)

\(u_{xx}-u_{t}\)

1.5550 (−05)

1.3987 (−05)

1.1042 (−05)

9.7392 (−03)

1.5641 (−02)

2.7121 (−02)

1/32

u

4.1496 (−08)

5.2605 (−08)

7.5414 (−08)

6.0229 (−04)

7.6836 (−04)

1.0785 (−03)

\(u_{xx}-u_{t}\)

9.6855 (−07)

8.7423 (−07)

6.8805 (−07)

2.4340 (−03)

3.9032 (−03)

6.7769 (−03)

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