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Theory and Modern Applications

Table 5 \(L_{1}\) and \(L_{\infty }\) errors and CPU time at some different values of time-step size k and spatial mesh size \(h=0.01\), \(\epsilon =0.01\) of Problem 2 using FTCS-ϵ, 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)

\(T_{\max }/53\)

2.8025 × 10−1

1.5265

1.488

\(T_{\max }/100\)

5.9959 × 10−2

6.6244 × 10−1

2.265

\(T_{\max }/200\)

2.1273 × 10−2

2.6296 × 10−1

4.704

\(T_{\max }/300\)

2.4401 × 10−3

3.1737 × 10−2

7.819

\(T_{\max }/310\)

9.7448 × 10−4

1.3521 × 10−2

8.154

\(T_{\max }/315\)

3.2771 × 10−4

4.7040 × 10−3

8.429

\(T_{\max }/320\)

4.6757 × 10−4

4.6218 ×10−3

8.537

\(T_{\max }/325\)

1.1657 × 10−3

1.2769 × 10−2

8.732

\(T_{\max }/350\)

4.5061 × 10−3

5.3608 × 10−2

9.779

\(T_{\max }/375\)

7.6305 × 10−3

9.1590 × 10−2

10.678

\(T_{\max }/400\)

1.0576 × 10−2

1.2682 × 10−1

11.692

\(T_{\max }/500\)

2.1076 × 10−2

2.4515 × 10−1

16.319

\(T_{\max }/600\)

3.0241 × 10−2

3.4502 × 10−1

21.644