Table 4 An evaluation of the accuracy of x (t) using NDsolve and ANN-PSO-NNA for case 1, with \({\varvec{\sigma}}\) = 0.1, \({\varvec{R}}=0.2\) and \({\varvec{B}}=0.3.\)
t | \({x(t)}_{Numerical}\) | \({\widehat{x}(t)}_{ANN}\) | \({AE(x(t))}_{ANN}\) |
---|---|---|---|
0 | 0 | 5.40E−06 | 5.4046E−06 |
0.1 | 0.009468358 | 0.009515209 | 4.6851E−05 |
0.2 | 0.017943263 | 0.017994147 | 5.0885E−05 |
0.3 | 0.025521751 | 0.025530937 | 9.1863E−06 |
0.4 | 0.0322914 | 0.032278219 | 1.3181E−05 |
0.5 | 0.038331266 | 0.038342661 | 1.1395E−05 |
0.6 | 0.043712682 | 0.043772499 | 5.9818E−05 |
0.7 | 0.048500038 | 0.048586562 | 8.6524E−05 |
0.8 | 0.052751446 | 0.052812704 | 6.1258E−05 |
0.9 | 0.056519362 | 0.056520039 | 6.7777E−07 |
1 | 0.05985115 | 0.059839029 | 1.212E−05 |