Table 5 Computed maximum point-wise error and rate of convergence for Example(1) at \(\varepsilon _{1}=10^{-6}\) and varying values of \(\varepsilon _{1}\)
\(\varepsilon _{2}\) | \(N=32\) | \(N=64\) | \(N=128\) | \(N=256\) | \(N=512\) | \(N=1024\) |
|---|---|---|---|---|---|---|
\(\downarrow\) | \(M=10\) | \(M=20\) | \(M=40\) | \(M=80\) | \(M=160\) | \(M=320\) |
\(10^{-6}\) | \(3.1504e-03\) | \(8.1321e-04\) | \(2.0669e-04\) | \(5.2012e-05\) | \(1.2694e-05\) | \(2.9297e-06\) |
1.9538 | 1.9762 | 1.9906 | 2.0347 | 2.1153 | − | |
\(10^{-8}\) | \(3.1503e-03\) | \(8.1313e-04\) | \(2.0666e-04\) | \(5.1994e-05\) | \(1.2686e-05\) | \(2.9270e-06\) |
1.9539 | 1.9762 | 1.9908 | 2.0351 | 2.1157 | − | |
\(10^{-10}\) | \(3.1503e-03\) | \(8.1313e-04\) | \(2.0666e-04\) | \(5.1994e-05\) | \(1.2686e-05\) | \(2.9269e-06\) |
1.9539 | 1.9762 | 1.9908 | 2.0351 | 2.1158 | − | |
\(10^{-12}\) | \(3.1503e-03\) | \(8.1313e-04\) | \(2.0666e-04\) | \(5.1994e-05\) | \(1.2686e-05\) | \(2.9269e-06\) |
1.9539 | 1.9762 | 1.9908 | 2.0351 | 2.1158 | − | |
\(10^{-14}\) | \(3.1503e-03\) | \(8.1313e-04\) | \(2.0666e-04\) | \(5.1994e-05\) | \(1.2686e-05\) | \(2.9269e-06\) |
1.9539 | 1.9762 | 1.9908 | 2.0351 | 2.1158 | − | |
\(E^{N,M}\) | \(3.1504e-03\) | \(8.1321e-04\) | \(2.0669e-04\) | \(5.2012e-05\) | \(1.2694e-05\) | \(2.9297e-06\) |
\({\overline{R}}^{N,M}\) | 1.9538 | 1.9762 | 1.9906 | 2.0347 | 2.1153 | − |