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Theory and Modern Applications

Table 5 Errors and convergence orders of scheme (59)–(61) and scheme (62)–(64) in the temporal direction (Example 2)

From: Numerical algorithms for multidimensional time-fractional wave equation of distributed-order with a nonlinear source term

τ

Scheme (59)–(61)

Scheme (62)–(64)

\(\|e^{N} \|_{L^{2}}\)

Order

CPU time

\(\|e^{N} \| _{L^{2}}\)

Order

CPU time

1/10

0.1869

\( 0.9506~\mbox{s} \)

0.1855

0.1057 s

1/20

0.0958

0.9642

\( 2.0467~\mbox{s} \)

0.0944

0.9746

0.1882 s

1/40

0.0488

0.9731

\( 4.8517~\mbox{s} \)

0.0474

0.9939

0.3908 s

1/80

0.0246

0.9882

\( 12.9781~\mbox{s} \)

0.0232

1.0308

0.7970 s

1/160

0.0123

1.0000

\( 39.2808~\mbox{s} \)

0.0108

1.1031

2.1005 s