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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

From: Unconditional stable numerical techniques for a water-quality model in a non-uniform flow stream

Δ x Δ t C (0.5, t ) \(\boldsymbol{\widetilde{C}(0.5,t)}\) \(\boldsymbol{\operatorname{error}(T_{\mathrm{mxe}})} \) \(\boldsymbol{T_{\mathrm{mxe}}}\)
0.0500 0.002500 0.9105 1.0961 0.1856 2.2775
0.0500 0.001250 0.9095 1.0889 0.1794 2.2738
0.0500 0.000625 0.9090 1.0654 0.1764 2.2719
0.0125 0.000625 0.5366 0.1289 0.4076 1.9513
0.0250 0.000625 0.0678 0.2856 0.2178 1.6856
0.1000 0.000625 0.9908 1.1121 0.1213 2.5000