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Table 9 \(L_{1}\) and \(L_{\infty }\) errors and CPU time at some different values of time-step size, k for Problem 2 at time \(2.5\times 10^{-3}\) with spatial mesh size, \(h=0.01\), \(\epsilon =0.01\) using NSFD-ϵ scheme, \(T_{\mathrm{max}}=2.5\times 10^{-3}\)

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)
\(T_{\max }/26\) 1.8636 × 10−1 9.8705 × 10−1 1.137
\(T_{\max }/50\) 1.2102 ×10−1 9.1868 × 10−1 1.485
\(T_{\max }/100\) 6.5470 × 10−2 6.7456 × 10−1 2.391
\(T_{\max }/200\) 2.4582 × 10−2 2.9094 × 10−1 4.880
\(T_{\max }/300\) 4.8806 × 10−3 5.9139 × 10−2 8.207
\(T_{\max }/333\) 1.0091 × 10−3 9.5627 × 10−3 9.437
\(T_{\max }/334\) 9.9448 × 10−4 1.0714 × 10−2 9.534
\(T_{\max }/335\) 1.0119 × 10−3 1.1866 × 10−2 9.540
\(T_{\max }/400\) 8.5987 × 10−3 1.0311 × 10−1 12.181
\(T_{\max }/500\) 1.9385 × 10−2 2.2445 × 10−1 17.074