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Table 3 \(L_{1}\) and \(L_{\infty }\) errors and CPU time at some different values of time-step size k for Problem 2 with \(\rho =10^{4}\) at time \(2.5\times 10^{-3}\) with spatial mesh size \(h=0.01\) using FTCS scheme, where \(T_{\max }=2.5\times 10^{-3}\)

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)
\(T_{\max }/52\) 2.8667 × 10−1 1.5040 1.368
\(T_{\max }/100\) 6.5144 × 10−2 6.9877 × 10−1 2.183
\(T_{\max }/200\) 3.2980 × 10−2 3.9927 × 10−1 4.532
\(T_{\max }/300\) 2.0727 × 10−2 2.5613 × 10−1 7.689
\(T_{\max }/400\) 1.4262 × 10−2 1.7830 × 10−1 11.509
\(T_{\max }/500\) 1.0268 × 10−2 1.2943 × 10−1 16.099
\(T_{\max }/600\) 7.5557 × 10−3 9.5605 × 10−2 22.270
\(T_{\max }/700\) 5.5929 × 10−3 7.1038 × 10−2 28.343
\(T_{\max }/800\) 4.1068 × 10−3 5.2473 × 10−2 35.383
\(T_{\max }/900\) 2.9425 × 10−3 3.7988 × 10−2 43.181
\(T_{\max }/1000\) 2.0059 × 10−3 2.6389 × 10−2 51.644
\(T_{\max }/1100\) 1.2404 × 10−3 1.6901 × 10−2 61.532
\(T_{\max }/1200\) 6.2983 × 10−4 9.0013 × 10−3 71.195
\(T_{\max }/1300\) 1.9347 × 10−4 2.3240 × 10−3 82.456
\(T_{\max }/1400\) 4.2509 × 10−4 4.3458 × 10−3 94.146
\(T_{\max }/1500\) 8.3336 × 10−4 8.7691 × 10−3 107.725
\(T_{\max }/1600\) 1.1913 × 10−3 1.3138 × 10−2 118.352