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Table 2 The error of \(\|\boldsymbol{u}^{r}-U^{r}\|\) and \(\|\boldsymbol{u}^{r}-U^{r}\|_{\infty}\) with \(r=\frac{0.8}{\tau}\)

From: Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen–Cahn equations

τ \(\|\boldsymbol{u}^{r}-U^{r}\|\) Rate \(\|\boldsymbol{u}^{r}-U^{r}\|_{\infty}\) Rate
1/50 2.3890e–06 4.3654e–06
1/100 6.1717e–07 1.9527 1.1288e–06 1.9513
1/200 1.5818e–07 1.9641 2.9042e–07 1.9586
1/400 4.1494e–08 1.9306 7.7267e–08 1.9102