Table 2 \(L_{1}\) and \(L_{\infty }\) errors and 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 \(h=0.01\) using FTCS scheme, where \(T_{\max }=2.5\times 10^{-3}\)

\(T_{\max }/52\)

2.8968 × 10⁻¹

1.5200

0.648

\(T_{\max }/100\)

6.5144 × 10⁻²

6.9877 × 10⁻¹

0.719

\(T_{\max }/200\)

3.2980 × 10⁻²

3.9927 × 10⁻¹

0.672

\(T_{\max }/300\)

2.0727 × 10⁻²

2.5613 × 10⁻¹

0.693

\(T_{\max }/400\)

1.4262 × 10⁻²

1.7830 × 10⁻¹

0.708

\(T_{\max }/500\)

1.0268 × 10⁻²

1.2943 × 10⁻¹

0.730

\(T_{\max }/600\)

7.5557 × 10⁻³

9.5605 × 10⁻²

0.770

\(T_{\max }/700\)

5.5929 × 10⁻³

7.1038 × 10⁻²

0.791

\(T_{\max }/800\)

4.1068 × 10⁻³

5.2473 × 10⁻²

0.816

\(T_{\max }/900\)

2.9425 × 10⁻³

3.7988 × 10⁻²

0.866

\(T_{\max }/1000\)

2.0059 × 10⁻³

2.6389 × 10⁻²

0.904

\(T_{\max }/1100\)

1.2404 × 10⁻³

1.6901 × 10⁻²

0.932

\(T_{\max }/1200\)

6.2983 × 10⁻⁴

9.0013 × 10⁻³

1.233

\(T_{\max }/1300\)

1.9347 × 10⁻⁴

2.3240 × 10⁻³

1.055

\(T_{\max }/1400\)

4.2509 × 10⁻⁴

4.3458 × 10⁻³

1.141

\(T_{\max }/1500\)

8.3336 × 10⁻⁴

8.7691 × 10⁻³

1.245

\(T_{\max }/1600\)

1.1913 × 10⁻³

1.3138 × 10⁻²

1.366