Table 2 Comparison of absolute errors for \(\Phi (\chi ,\tau )\) and \(\Psi (\chi ,\tau )\) in Problem 1 when \(\xi =2\), \(\zeta =3\), \(\mu =1\).
\(\chi\) | \(\tau\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{C}}|\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{CF}}|\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{AB}}|\) | NTIM41 | OHAM41 |
|---|---|---|---|---|---|---|
0.1 | 2.78454 \(e-\)10 | 2.78454 \(e-\)10 | 2.78454 \(e-\)10 | 3.46778 \(e-\)07 | 3.27824 \(e-\)05 | |
0.001 | 0.3 | 1.7778\(e-\)10 | 1.7778\(e-\)10 | 1.7778\(e-\)10 | 3.79106\(e-\)07 | 3.00729\(e-\)05 |
0.5 | 7.63204\(e-\)11 | 7.63204\(e-\)11 | 7.63204\(e-\)11 | 3.97046\(e-\)07 | 2.71800\(e-\)05 | |
0.1 | 7.54153\(e-\)09 | 7.54153\(e-\)09 | 7.54153\(e-\)09 | 3.11923\(e-\)06 | 9.56651\(e-\)05 | |
0.003 | 0.3 | 4.8245\(e-\)09 | 4.8245\(e-\)09 | 4.8245\(e-\)09 | 3.41148\(e-\)06 | 8.76522\(e-\)05 |
0.5 | 2.08434\(e-\)09 | 2.08434\(e-\)09 | 2.08434\(e-\)09 | 3.57426\(e-\)06 | 7.91159\(e-\)05 | |
0.1 | 3.5022\(e-\)08 | 3.5022\(e-\)08 | 3.5022\(e-\)08 | 8.65953\(e-\)06 | 1.54961\(e-\)04 | |
0.005 | 0.3 | 2.24488\(e-\)08 | 2.24488\(e-\)08 | 2.24488\(e-\)08 | 9.47491\(e-\)06 | 1.41802\(e-\)04 |
0.5 | 9.75955\(e-\)09 | 9.75955\(e-\)09 | 9.75955\(e-\)09 | 9.93078\(e-\)06 | 1.27816\(e-\)04 | |
0.1 | 9.6395\(e-\)08 | 9.6395\(e-\)08 | 9.6395\(e-\)08 | 1.69627\(e-\)05 | 2.10655\(e-\)04 | |
0.007 | 0.3 | 6.19098\(e-\)08 | 6.19098\(e-\)08 | 6.19098\(e-\)08 | 1.85679\(e-\)05 | 1.92514\(e-\)04 |
0.5 | 2.70818\(e-\)08 | 2.70818\(e-\)08 | 2.70818\(e-\)08 | 1.94686\(e-\)05 | 1.73277\(e-\)04 |
\(\chi\) | \(\tau\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{C}}|\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{CF}}|\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{AB}}|\) | NTIM41 | OHAM41 |
|---|---|---|---|---|---|---|
0.1 | 2.78454\(e-10\) | 2.78454\(e-10\) | 2.78454\(e-10\) | 3.46778\(e-07\) | 1.18952\(e-06\) | |
0.001 | 0.3 | 1.7778\(e-10\) | 1.7778\(e-10\) | 1.7778\(e-10\) | 3.79106\(e-07\) | 1.13777\(e-06\) |
0.5 | 7.63203\(e-11\) | 7.63203\(e-11\) | 7.63203\(e-11\) | 3.97046\(e-07\) | 1.06865\(e-06\) | |
0.1 | 7.54153\(e-09\) | 7.54153\(e-09\) | 7.54153\(e-09\) | 3.11923\(e-06\) | 7.39727\(e-06\) | |
0.003 | 0.3 | 4.8245\(e-09\) | 4.8245\(e-09\) | 4.8245\(e-09\) | 3.41148\(e-06\) | 7.20459\(e-06\) |
0.5 | 2.08434\(e-09\) | 2.08434\(e-09\) | 2.08434\(e-09\) | 3.57426\(e-06\) | 6.87421\(e-06\) | |
0.1 | 3.5022\(e-08\) | 3.5022\(e-08\) | 3.5022\(e-08\) | 8.65953\(e-06\) | 1.86987\(e-05\) | |
0.005 | 0.3 | 2.24488\(e-08\) | 2.24488\(e-08\) | 2.24488\(e-08\) | 9.47491\(e-06\) | 1.83192\(e-05\) |
0.5 | 9.75955\(e-09\) | 9.75955\(e-09\) | 9.75955\(e-09\) | 9.93078\(e-06\) | 1.75676\(e-05\) | |
0.1 | 9.6395\(e-08\) | 9.6395\(e-08\) | 9.6395\(e-08\) | 1.69627\(e-05\) | 3.50801\(e-05\) | |
0.007 | 0.3 | 6.19098\(e-08\) | 6.19098\(e-08\) | 6.19098\(e-08\) | 1.85679\(e-05\) | 3.44727\(e-05\) |
0.5 | 2.70818\(e-08\) | 2.70818\(e-08\) | 2.70818\(e-08\) | 1.94686\(e-05\) | 3.31448\(e-05\) |
