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Theory and Modern Applications

Table 2 The absolute errors for the nonhomogenous fourth-order parabolic equation ( 69 ), Example 2

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

Methods

λ

Time steps

 

x  = 0.1

x  = 0.2

x  = 0.3

x  = 0.4

x  = 0.5

Proposed \(O(k^{2}+h^{4})\)-

method (28a)-(28b)

0.5

16

u

2.09 (−11)

2.63 (−11)

1.23 (−10)

1.93 (−10)

2.85 (−10)

\(u_{xx}\)

5.06 (−09)

1.54 (−08)

6.00 (−08)

3.40 (−08)

3.87 (−08)

\(O(k^{2}+h^{4})\)-method in [33]

0.5

16

u

7.46 (−10)

2.91 (−10)

8.65 (−10)

6.87 (−10)

6.98 (−10)

\(O(k^{4}+h^{4})\)-method in [33]

0.5

16

u

6.25 (−10)

2.22 (−10)

4.53 (−10)

4.41 (−10)

5.03 (−10)