Theory and Modern Applications
Table 8 \(L_{1}\) and \(L_{\infty }\) errors and CPU time at some different values of time-step size k for Problem 1 at time \(2.5\times 10^{-3}\) with spatial mesh size \(h=0.01\), \(\epsilon =0.01\) using NSFD-ϵ scheme, \(T_{\max }=2.5\times 10^{-3}\)
Time step (k) | \(L_{1}\) error | \(L_{\infty }\) error | CPU (s) |
|---|---|---|---|
\(T_{\max }/26\) | 1.8636 × 10−1 | 9.8705 × 10−1 | 0.653 |
\(T_{\max }/50\) | 1.2102 ×10−1 | 9.1868 × 10−1 | 0.662 |
\(T_{\max }/100\) | 6.5470 × 10−2 | 6.7456 × 10−1 | 0.670 |
\(T_{\max }/200\) | 2.4582 × 10−2 | 2.9094 × 10−1 | 0.682 |
\(T_{\max }/300\) | 4.8806 × 10−3 | 5.9139 × 10−2 | 0.699 |
\(T_{\max }/333\) | 1.0091 × 10−3 | 9.5627 × 10−3 | 0.715 |
\(T_{\max }/334\) | 9.9448 × 10−4 | 1.0714 × 10−2 | 0.707 |
\(T_{\max }/335\) | 1.0119 × 10−3 | 1.1866 × 10−2 | 0.787 |
\(T_{\max }/400\) | 8.5987 × 10−3 | 1.0311 × 10−1 | 0.722 |
\(T_{\max }/500\) | 1.9385 × 10−2 | 2.2445 × 10−1 | 0.780 |