Table 1 Numeric results for \(\theta = 0.6\) for Example 1.

From: Analytical and numerical solutions of MABC fractional advection dispersion models by utilizing the modified physics informed neural networks with impacts of fractional derivative

\((y, t)\)

Approximate

Exact

Absolute error (PINN)

Error in56

Error in57

(0.2, 0.2)

0.02351

0.02351

\(6.79 \times 10^{-11}\)

\(1.4945 \times 10^{-10}\)

\(6.2970 \times 10^{-5}\)

(0.4, 0.4)

0.1521

0.1521

\(4.03 \times 10^{-10}\)

\(5.9758 \times 10^{-10}\)

\(1.4247 \times 10^{-4}\)

(0.6, 0.6)

0.3423

0.3423

\(8.52 \times 10^{-10}\)

\(1.2002 \times 10^{-9}\)

\(1.4987 \times 10^{-4}\)

(0.8, 0.8)

0.3761

0.3761

\(8.90 \times 10^{-10}\)

\(1.8295 \times 10^{-9}\)

\(1.4253 \times 10^{-4}\)

Back to article page