Table 8 Periodic case: Computed invariant quantities and errors in the ${\mathit{l}}^{\mathbf{\infty }}$ -norm and the ${\mathit{L}}^{\mathbf{2}}$ -norm ( $\mathit{h}\mathbf{=}\mathbf{0.05}$ , $\mathit{\tau }\mathbf{=}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$ )

Method

Time

${\mathbf{err}}^{\mathbf{\infty }}$

${\mathbf{err}}^{\mathbf{0}}$

${\mathit{I}}_{\mathit{M}}\mathbf{(}{\mathit{u}}_{\mathit{h}}^{\mathit{l}}\mathbf{)}$

${\mathit{I}}_{\mathit{P}}\mathbf{(}{\mathit{u}}_{\mathit{h}}^{\mathit{l}}\mathbf{)}$

${\mathit{I}}_{\mathit{E}}\mathbf{(}{\mathit{u}}_{\mathit{h}}^{\mathit{l}}\mathbf{)}$