Table 12 An evaluation of the accuracy of z (t) using NDsolve and ANN-PSO-NNA for case 1, with \({\varvec{\sigma}}\) = 0.1, R = 0.2 and B = 0.3.

From: Neuro-computing solution for Lorenz differential equations through artificial neural networks integrated with PSO-NNA hybrid meta-heuristic algorithms: a comparative study

t

\({z(t)}_{Numerical}\)

\({\widehat{z}(t)}_{ANN}\)

\({AE(z(t))}_{ANN}\)

0

0

4.00E−05

3.99963E−05

0.1

0.003987329

0.004023065

3.57361E−05

0.2

0.012902208

0.012927978

2.57704E−05

0.3

0.023826656

0.023863057

3.64013E−05

0.4

0.035274975

0.035339763

6.4788E−05

0.5

0.046564683

0.046655244

9.05611E−05

0.6

0.05745071

0.057543985

9.32752E−05

0.7

0.067915471

0.067981618

6.61468E−05

0.8

0.078050717

0.07807296

2.22425E−05

0.9

0.087992822

0.087985296

7.52576E−06

1

0.097888752

0.097904612

1.58602E−05

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