Table 1 Computed \(E_{\varepsilon _{1},\varepsilon _{2}}^{N,M},E^{N,M},{\overline{R}}_{\varepsilon _{2},\varepsilon _{2}}^{N,M}\) and \({\overline{R}}^{N,M}\) for Example (1) at \(\varepsilon _{2}=10^{-6}\)
\(\varepsilon _{1}\) | \(N=M=16\) | \(N=M=32\) | \(N=M=64\) | \(N=M=128\) | \(N=M=256\) | \(N=M=512\) |
|---|---|---|---|---|---|---|
\(\downarrow\) | ||||||
\(10^{-4}\) | \(1.6273e-02\) | \(4.3478e-03\) | \(1.1160e-03\) | \(2.8003e-04\) | \(6.9103e-05\) | \(1.7015e-05\) |
1.9041 | 1.9619 | 1.9947 | 2.0188 | 2.0219 | − | |
\(10^{-6}\) | \(1.6372e-02\) | \(4.3839e-03\) | \(1.1325e-03\) | \(2.8759e-04\) | \(7.2394e-05\) | \(1.8152e-05\) |
1.9009 | 1.9527 | 1.9774 | 1.9901 | 1.9957 | − | |
\(10^{-8}\) | \(1.6374e-02\) | \(4.3846e-03\) | \(1.1328e-03\) | \(2.8773e-04\) | \(7.2451e-05\) | \(1.8177e-05\) |
1.9009 | 1.9526 | 1.9771 | 1.9896 | 1.9949 | − | |
\(10^{-10}\) | \(1.6374e-02\) | \(4.3846e-03\) | \(1.1328e-03\) | \(2.8776e-04\) | \(7.2480e-05\) | \(1.8195e-05\) |
1.9009 | 1.9526 | 1.9770 | 1.9892 | 1.9940 | − | |
\(10^{-12}\) | \(1.6374e-02\) | \(4.3846e-03\) | \(1.1328e-03\) | \(2.8776e-04\) | \(7.2480e-05\) | \(1.8195e-05\) |
1.9009 | 1.9526 | 1.9770 | 1.9892 | 1.9940 | − | |
\(10^{-14}\) | \(1.6374e-02\) | \(4.3846e-03\) | \(1.1328e-03\) | \(2.8776e-04\) | \(7.2480e-05\) | \(1.8195e-05\) |
1.9009 | 1.9526 | 1.9770 | 1.9892 | 1.9940 | − | |
\(E^{N,M}\) | \(1.6374e-02\) | \(4.3846e-03\) | \(1.1328e-03\) | \(2.8776e-04\) | \(7.2480e-05\) | \(1.8195e-05\) |
\({\overline{R}}^{N,M}\) | 1.9009 | 1.9526 | 1.9770 | 1.9892 | 1.9940 | − |