Theory and Modern Applications
Table 4 Approximate solutions using RK4 (first row) and numerical technique (59) (second row, \(\varOmega = 0.98\)) with step-size \(h=10^{-3}\) over \([0, 10]\) for \(X(0)=Y(0)=V(0)=20\) having parameter \(p=6\)
Solution | t = 0 | t = 2 | t = 4 | t = 6 | t = 8 | t = 10 |
|---|---|---|---|---|---|---|
\(X_{t}\) | 2.0000e+01 | 8.3821e+00 | 6.0235e+00 | 6.6745e+00 | 8.2887e+00 | 1.0300e+01 |
2.0000e+01 | 8.6224e+00 | 6.3305e+00 | 6.8376e+00 | 8.2317e+00 | 9.9723e+00 | |
\(Y_{t}\) | 2.0000e+01 | 1.6589e+01 | 9.7699e+00 | 5.5563e+00 | 3.4266e+00 | 2.3859e+00 |
2.0000e+01 | 1.6521e+01 | 1.0108e+01 | 6.0760e+00 | 3.9577e+00 | 2.8768e+00 | |
\(V_{t}\) | 2.0000e+01 | 1.4282e+02 | 8.5516e+01 | 4.8488e+01 | 2.9634e+01 | 2.0405e+01 |
2.0000e+01 | 1.4174e+02 | 8.8162e+01 | 5.2874e+01 | 3.4167e+01 | 2.4592e+01 |