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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 7 The MAEs for the good Boussinesq equation ( 5 ), Example 7 at various time levels for a uniform mesh with \(\pmb{k=0.05}\)

t	Parameters		\(\boldsymbol {O(k^{2}+h^{4})}\) -method ( 28a )-( 28b )		Collocation method discussed in [ 36 ]
t	Parameters		u	\(\boldsymbol {u_{xx}}\)	u
0.5	h = 1/40	\(x_{0}=30\)	8.1007 (−07)	4.4585 (−06)	8.2943 (−07)
1.0	h = 1/60	\(x_{0}=40\)	7.6030 (−09)	3.1598 (−08)	7.3326 (−09)
1.5	h = 1/80	\(x_{0}=50\)	5.8974 (−11)	2.0970 (−09)	6.4525 (−11)
2.0	h = 1/100	\(x_{0}=60\)	2.9068 (−13)	3.2836 (−13)	5.2066 (−13)