Table 1 The error defined by \(\pmb{\operatorname{error}(T_{\mathrm{mxe}}) = \max \vert C(0.50,t)-\widetilde{C}(0.5,t) \vert }\) for all \(\pmb{0\leq t \leq 5}\) , for some \(\pmb{T_{\mathrm{mxe}}\in [0,5]}\) , where C and \(\pmb{\widetilde{C}}\) are theoretical solutions and new fourth-order scheme solutions, respectively

Δ x

Δ t

C (0.5, t )

\(\boldsymbol{\widetilde{C}(0.5,t)}\)

\(\boldsymbol{\operatorname{error}(T_{\mathrm{mxe}})} \)

\(\boldsymbol{T_{\mathrm{mxe}}}\)