Theory and Modern Applications
Table 2 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 \(X(0)=1\), \(Y(0)=2\), \(V(0)=40\) having parameter \(k=0\)
Solution | t = 0 | t = 2 | t = 4 | t = 6 | t = 8 | t = 10 |
|---|---|---|---|---|---|---|
\(X_{t}\) | 1.0000e+00 | 4.8558e+00 | 8.7192e+00 | 1.2507e+01 | 1.6219e+01 | 1.9859e+01 |
1.0000e+00 | 4.8420e+00 | 8.6224e+00 | 1.2311e+01 | 1.5915e+01 | 1.9441e+01 | |
\(Y_{t}\) | 2.0000e+00 | 7.7616e−01 | 2.8586e−01 | 1.0516e−01 | 3.8687e−02 | 1.4232e−02 |
2.0000e+00 | 7.8834e−01 | 3.0603e−01 | 1.2332e−01 | 5.2975e−02 | 2.5252e−02 | |
\(V_{t}\) | 4.0000e+01 | 9.9150e−02 | 2.4577e−04 | 6.0920e−07 | 1.5101e−09 | 3.7430e−12 |
4.0000e+01 | 2.2535e−01 | 4.2880e−02 | 2.6096e−02 | 1.8916e−02 | 1.4857e−02 |