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Table 10 \(L_{1}\) and \(L_{\infty }\) errors CPU time at some different values of time-step size k for Problem 1 with \(\rho =10^{4}\) at time \(2.5\times 10^{-3}\) with spatial mesh size \(\sigma =2.0 \) and \(h=0.01\) using FTCS with artificial viscosity

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)
\(T_{\max }/53\) 2.6947 × 10−1 1.5155 0.737
\(T_{\max }/100\) 6.2546 × 10−2 6.8175 × 10−1 0.737
\(T_{\max }/200\) 3.0034 × 10−2 3.6771 × 10−1 0.742
\(T_{\max }/300\) 1.7645 × 10−2 2.1809 × 10−1 0.758
\(T_{\max }/400\) 1.1108 × 10−2 1.3983 × 10−1 0.782
\(T_{\max }/500\) 7.0695 × 10−3 8.9529 × 10−2 0.800
\(T_{\max }/600\) 4.3263 × 10−3 5.5222 × 10−2 0.847
\(T_{\max }/700\) 2.3414 × 10−3 3.0552 × 10−2 0.856
\(T_{\max }/800\) 8.5592 × 10−4 1.2040 × 10−2 0.907
\(T_{\max }/850\) 3.1048 × 10−4 4.4291 × 10−3 0.913
\(T_{\max }/860\) 2.2700 × 10−4 3.0141 × 10−3 0.918
\(T_{\max }/870\) 1.6308 × 10−4 1.8608 × 10−3 0.923
\(T_{\max }/880\) 1.3833 × 10−4 2.3032 × 10−3 0.926
\(T_{\max }/890\) 2.3267 × 10−4 2.9465 × 10−3 0.930
\(T_{\max }/900\) 3.3881 × 10−4 3.6042 × 10−3 0.951
\(T_{\max }/1000\) 1.2861 × 10−3 1.4273 × 10−2 0.967
\(T_{\max }/1100\) 2.0648 × 10−3 2.3789 × 10−2 1.001
\(T_{\max }/1200\) 2.7162 × 10−3 3.1756 × 10−2 1.042
\(T_{\max }/1300\) 3.2692 × 10−3 3.8522 × 10−2 1.071
\(T_{\max }/1400\) 3.7445 × 10−3 4.4336 × 10−2 1.124
\(T_{\max }/1500\) 4.1573 × 10−3 4.9385 × 10−3 1.142