Skip to main content

Theory and Modern Applications

Table 6 The MAEs for the second-order Benjamin-Ono equation ( 4 ) with \(\pmb{q=1, r=-1}\) , Example 6 at various time levels for \(\pmb{h=0.1, k=0.01}\)

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

t

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

Method discussed in [ 7 ]

u

\(\boldsymbol {u_{xx}}\)

u

5

4.2188 (−07)

2.4846 (−07)

3.3988 (−04)

10

1.8157 (−06)

8.2387 (−07)

5.2273 (−04)

15

5.5052 (−06)

2.4263 (−06)

8.2328 (−04)

20

1.4255 (−05)

6.2847 (−06)

1.2596 (−03)