Theory and Modern Applications
Table 3 Approximate solutions using RK4 (first row) and numerical technique (59) (second row, \(\varOmega = 0.99\)) with step-size \(h=10^{-3}\) over \([0, 10]\) for \(X(0)=10\), \(Y(0)=10\), \(V(0)=0\) having parameters \(k=5\), \(p=0\)
Solution | t = 0 | t = 2 | t = 4 | t = 6 | t = 8 | t = 10 |
|---|---|---|---|---|---|---|
\(X_{t}\) | 1.0000e+01 | 1.0401e+01 | 7.0138e+00 | 3.7920e+00 | 2.2327e+00 | 1.6525e+00 |
1.0000e+01 | 1.0364e+01 | 7.0442e+00 | 3.8876e+00 | 2.3160e+00 | 1.7078e+00 | |
\(Y_{t}\) | 1.0000e+01 | 6.1286e+00 | 6.8936e+00 | 6.9577e+00 | 5.9635e+00 | 5.0381e+00 |
1.0000e+01 | 6.1771e+00 | 6.9000e+00 | 6.9722e+00 | 6.0372e+00 | 5.1345e+00 | |
\(V_{t}\) | 0.0000e+00 | 7.2562e+01 | 1.3702e+02 | 2.0754e+02 | 2.7250e+02 | 3.2717e+02 |
0.0000e+00 | 7.2356e+01 | 1.3578e+02 | 2.0457e+02 | 2.6791e+02 | 3.2139e+02 |