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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Overview of the numerical results for the example IVPs in Eq. (29)–Eq. (32), where \(\ell _{1}\)- and \(\ell _{\infty}\)-error are shown for IVPs with an exact solution given, (h) total number of learned subdomains

From: Adaptive neural-domain refinement for solving time-dependent differential equations

Example

Domain

h

\(\ell _{1}\)-error

\(\ell _{\infty}\)-error

IVP in Eq. (29)

t∈[0,15]

113

1.4499e-4

1.9268e-4

IVP in Eq. (30)

t∈[0,25]

50

6.8152e-4

9.8980e-4

IVP in Eq. (31)

t∈[0,20]

32

4.6545e-3

4.9861e-3

IVP in Eq. (32)

t∈[0,30]

51

–

–

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