Table 3 Comparison of absolute errors for \(\Phi (\chi ,\tau )\) and \(\Psi (\chi ,\tau )\) in Problem 2 when \(\xi =2\), \(\zeta =2\), \(\mu =1\).
\(\chi\) | \(\tau\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{C}}|\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{CF}}|\) | \(|\Phi ^{\texttt{Exact}}-\Phi ^{\texttt{AB}}|\) | FRDTM34 | q-HATM34 |
|---|---|---|---|---|---|---|
0 | 0.01 | 2.71078\(e-12\) | 2.71033\(e-12\) | 2.71078\(e-12\) | 2.71072\(e-12\) | 2.07040\(e-12\) |
0.03 | 6.73927\(e-10\) | 6.73926\(e-10\) | 6.73927\(e-10\) | 6.73927\(e-10\) | 6.73927\(e-10\) | |
0.05 | 8.86033\(e-09\) | 8.86033\(e-09\) | 8.86033\(e-09\) | 8.86033\(e-09\) | 8.86033\(e-09\) | |
1 | 0.01 | 3.21043\(e-12\) | 3.21060\(e-12\) | 3.21043\(e-12\) | 3.21052\(e-12\) | 3.21051\(e-12\) |
0.03 | 7.72406\(e-10\) | 7.72406\(e-10\) | 7.72406\(e-10\) | 7.72406\(e-10\) | 7.72406\(e-10\) | |
0.05 | 9.82970\(e-09\) | 9.82970\(e-09\) | 9.82970\(e-09\) | 9.82970\(e-09\) | 9.82970\(e-09\) | |
2 | 0.01 | 3.00746\(e-12\) | 3.00693\(e-12\) | 3.00746\(e-12\) | 3.00748\(e-12\) | 3.00748\(e-12\) |
0.03 | 7.36736\(e-10\) | 7.36735\(e-10\) | 7.36736\(e-10\) | 7.36736\(e-10\) | 7.36736\(e-10\) | |
0.05 | 9.54952\(e-09\) | 9.54953\(e-09\) | 9.54952\(e-09\) | 9.54952\(e-09\) | 9.54952\(e-09\) | |
3 | 0.01 | 4.48808\(e-13\) | 4.48114\(e-13\) | 4.48808\(e-13\) | 4.48808\(e-13\) | 4.48808\(e-13\) |
0.03 | 1.13509\(e-10\) | 1.13508\(e-10\) | 1.13509\(e-10\) | 1.13509\(e-10\) | 1.13509\(e-10\) | |
0.05 | 1.51797\(e-09\) | 1.51797\(e-09\) | 1.51797\(e-09\) | 1.51797\(e-09\) | 1.51797\(e-09\) | |
4 | 0.01 | 5.04097\(e-13\) | 5.04558\(e-13\) | 5.04097\(e-13\) | 5.04100\(e-13\) | 5.04100\(e-13\) |
0.03 | 1.21954\(e-10\) | 1.21955\(e-10\) | 1.21954\(e-10\) | 1.21954\(e-10\) | 1.21954\(e-10\) | |
0.05 | 1.56086\(e-09\) | 1.56086\(e-09\) | 1.56086\(e-09\) | 1.56086\(e-09\) | 1.56086\(e-09\) |
\(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{C}}|\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{CF}}|\) | \(|\Psi ^{\texttt{Exact}}-\Psi ^{\texttt{AB}}|\) | FRDTM34 | q-HATM34 | ||
|---|---|---|---|---|---|---|
0 | 0.01 | 1.35539\(e-12\) | 1.35547\(e-12\) | 1.35539\(e-12\) | 1.35536\(e-12\) | 1.35536\(e-12\) |
0.03 | 3.36964\(e-10\) | 3.36964\(e-10\) | 3.36964\(e-10\) | 3.36964\(e-10\) | 3.36964\(e-10\) | |
0.05 | 4.43017\(e-09\) | 4.43017\(e-09\) | 4.43017\(e-09\) | 4.43017\(e-09\) | 4.43017\(e-09\) | |
1 | 0.01 | 1.60522\(e-12\) | 1.60510\(e-12\) | 1.60522\(e-12\) | 1.60526\(e-12\) | 1.60526\(e-12\) |
0.03 | 3.86203\(e-10\) | 3.86203\(e-10\) | 3.86203\(e-10\) | 3.86203\(e-10\) | 3.86203\(e-10\) | |
0.05 | 4.91485\(e-09\) | 4.91485\(e-09\) | 4.91485\(e-09\) | 4.91485\(e-09\) | 4.91485\(e-09\) | |
2 | 0.01 | 1.50373\(e-12\) | 1.50362\(e-12\) | 1.50373\(e-12\) | 1.50374\(e-12\) | 1.50374\(e-12\) |
0.03 | 3.68368\(e-10\) | 3.68368\(e-10\) | 3.68368\(e-10\) | 3.68368\(e-10\) | 3.68368\(e-10\) | |
0.05 | 4.77476\(e-09\) | 4.77476\(e-09\) | 4.77476\(e-09\) | 4.77476\(e-09\) | 4.77476\(e-09\) | |
3 | 0.01 | 2.24404\(e-13\) | 2.24336\(e-13\) | 2.24404\(e-13\) | 2.24404\(e-13\) | 2.24404\(e-13\) |
0.03 | 5.67546\(e-11\) | 5.67546\(e-11\) | 5.67546\(e-11\) | 5.67546\(e-11\) | 5.67546\(e-11\) | |
0.05 | 7.58984\(e-10\) | 7.58984\(e-10\) | 7.58984\(e-10\) | 7.58984\(e-10\) | 7.58984\(e-10\) | |
4 | 0.01 | 2.52048\(e-13\) | 2.52081\(e-13\) | 2.52048\(e-13\) | 2.52050\(e-13\) | 2.52050\(e-13\) |
0.03 | 6.09771\(e-11\) | 6.09771\(e-11\) | 6.09771\(e-11\) | 6.09771\(e-11\) | 6.09771\(e-11\) | |
0.05 | 7.80430\(e-10\) | 7.80430\(e-10\) | 7.80430\(e-10\) | 7.80430\(e-10\) | 7.80430\(e-10\) |
