Table 4 Comparison of absolute errors for \(\Phi (\chi ,\tau )\) and \(\Psi (\chi ,\tau )\) in Problem 2 when \(\xi =2\), \(\zeta =2\), \(\mu =1\).
\(\chi\) | \(\tau\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{C}}|\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{CF}}|\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{AB}}|\) | NTIM41 | OHAM41 |
|---|---|---|---|---|---|---|
0.001 | 0.1 | 8.51031 \(e-\)11 | 8.51031 \(e-\)11 | 8.51031 \(e-\)11 | 2.38719 \(e-\)11 | 2.88115\(e-\)06 |
0.3 | 6.09674\(e-\)11 | 6.09674\(e-\)11 | 6.09674\(e-\)11 | 3.42036\(e-\)11 | 2.70417\(e-\)06 | |
0.5 | 3.62378\(e-\)11 | 3.62378\(e-\)11 | 3.62378\(e-\)11 | 4.52451\(e-\)11 | 2.51242\(e-\)06 | |
0.003 | 0.1 | 2.30234\(e-\)09 | 2.30234\(e-\)09 | 2.30234\(e-\)09 | 6.39987\(e-\)10 | 1.02084\(e-\)05 |
0.3 | 1.65092\(e-\)09 | 1.65092\(e-\)09 | 1.65092\(e-\)09 | 9.18695\(e-\)10 | 9.64541\(e-\)06 | |
0.5 | 9.83212\(e-\)10 | 9.83212\(e-\)10 | 9.83212\(e-\)10 | 1.21683\(e-\)09 | 9.0176\(e-\)06 | |
0.005 | 0.1 | 1.06800\(e-\)08 | 1.06800\(e-\)08 | 1.06800\(e-\)08 | 2.94183\(e-\)09 | 1.9619\(e-\)05 |
0.3 | 7.6654\(e-\)09 | 7.6654\(e-\)09 | 7.6654\(e-\)09 | 4.23099\(e-\)09 | 1.86281\(e-\)05 | |
0.5 | 4.57410\(e-\)09 | 4.57410\(e-\)09 | 4.57410\(e-\)09 | 5.61126\(e-\)09 | 1.74951\(e-\)05 | |
0.007 | 0.1 | 2.93638\(e-\)08 | 2.93638\(e-\)08 | 2.93638\(e-\)08 | 8.01463\(e-\)09 | 3.11086\(e-\)05 |
0.3 | 2.10948\(e-\)08 | 2.10948\(e-\)08 | 2.10948\(e-\)08 | 1.15488\(e-\)08 | 2.96491\(e-\)05 | |
0.5 | 1.26122\(e-\)08 | 1.26122\(e-\)08 | 1.26122\(e-\)08 | 1.53364\(e-\)08 | 2.79431\(e-\)05 |
\(\chi\) | \(\tau\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{C}}|\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{CF}}|\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{AB}}|\) | NTIM41 | OHAM41 |
|---|---|---|---|---|---|---|
0.001 | 0.1 | 4.25514\(e-11\) | 4.25514\(e-11\) | 4.25514\(e-11\) | 1.1936\(e-11\) | 8.90479\(e-06\) |
0.3 | 3.04836\(e-11\) | 3.04836\(e-11\) | 3.04836\(e-11\) | 1.71018\(e-11\) | 8.31684\(e-06\) | |
0.5 | 1.81189\(e-11\) | 1.81189\(e-11\) | 1.81189\(e-11\) | 2.26226\(e-11\) | 7.69092\(e-06\) | |
0.003 | 0.1 | 1.15117\(e-09\) | 1.15117\(e-09\) | 1.15117\(e-09\) | 3.19993\(e-10\) | 2.62487\(e-05\) |
0.3 | 8.25461\(e-10\) | 8.25461\(e-10\) | 8.25461\(e-10\) | 4.59347\(e-10\) | 2.44863\(e-05\) | |
0.5 | 4.91606\(e-10\) | 4.91606\(e-10\) | 4.91606\(e-10\) | 6.08413\(e-10\) | 2.26156\(e-06\) | |
0.005 | 0.1 | 5.34002\(e-09\) | 5.34002\(e-09\) | 5.34002\(e-09\) | 1.47092\(e-09\) | 4.29701\(e-05\) |
0.3 | 3.83270\(e-09\) | 3.83270\(e-09\) | 3.83270\(e-09\) | 2.11549\(e-09\) | 4.00354\(e-05\) | |
0.5 | 2.28705\(e-09\) | 2.28705\(e-09\) | 2.28705\(e-09\) | 2.80563\(e-09\) | 3.69301\(e-05\) | |
0.007 | 0.1 | 1.46819\(e-08\) | 1.46819\(e-08\) | 1.46819\(e-08\) | 4.00732\(e-09\) | 5.90667\(e-05\) |
0.3 | 1.05474\(e-08\) | 1.05474\(e-08\) | 1.05474\(e-08\) | 5.77442\(e-09\) | 5.49628\(e-05\) | |
0.5 | 6.30612\(e-09\) | 6.30612\(e-09\) | 6.30612\(e-09\) | 7.6682\(e-09\) | 5.06334\(e-05\) |
