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Table 11 \(L_{1}\) and \(L_{\infty }\) errors and CPU time at some different values of time step size k for Problem 1 at time \(2.5\times 10^{-3}\) with spatial mesh size \(h=0.01\), \(\sigma =2.0\) using NSFD with artificial viscosity method

From: On the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction term

Time step (k) \(L_{1}\) error \(L_{\infty }\) error CPU (s)
\(T_{\max }/25\) 1.8982 × 10−1 9.8811 × 10−1 0.891
\(T_{\max }/50\) 1.2102 × 10−1 9.1869 × 10−1 0.893
\(T_{\max }/100\) 6.8010 × 10−2 6.9128 × 10−1 0.897
\(T_{\max }/200\) 3.3252 × 10−2 3.8653 × 10−1 0.928
\(T_{\max }/300\) 1.9973 × 10−2 2.4143 × 10−1 0.998
\(T_{\max }/400\) 1.2961 × 10−2 1.5892 × 10−1 0.999
\(T_{\max }/500\) 8.6255 × 10−3 1.0838 × 10−1 1.019
\(T_{\max }/600\) 5.6799 × 10−3 7.3290 × 10−2 1.041
\(T_{\max }/700\) 3.5494 × 10−3 4.7746 × 10−2 1.089
\(T_{\max }/800\) 1.9544 × 10−3 2.8406 × 10−2 1.355
\(T_{\max }/900\) 8.4110 × 10−4 1.3294 × 10−2 1.355
\(T_{\max }/950\) 5.2648 × 10−4 7.1035 × 10−3 1.564
\(T_{\max }/1000\) 4.4308 × 10−4 5.5908 × 10−3 1.664
\(T_{\max }/1050\) 7.8758 × 10−4 8.5810 × 10−3 1.683
\(T_{\max }/1100\) 1.1865 × 10−3 1.1836 × 10−2 1.684
\(T_{\max }/1200\) 1.8866 × 10−3 1.9106 × 10−2 1.687
\(T_{\max }/1300\) 2.4809 × 10−3 2.5706 × 10−2 1.688
\(T_{\max }/1400\) 2.9918 × 10−3 3.1732 × 10−2 1.690
\(T_{\max }/1500\) 3.4356 × 10−3 3.6977 × 10−2 1.745