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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 6 Errors and convergence orders of scheme (59)–(61) with an optimal step size ratio for τ, \(h_{1}\), \(h_{2}\), \(h_{3}\) and Δβ (Example 2)

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

τ

\(h_{1}=h_{2}=h_{3}\)

Δβ

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

Order

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

Order

CPU time

1/16

π/4

1/4

0.1717

–

0.0998

–

\( 0.0285~\mbox{s} \)

1/64

π/8

1/8

0.0435

1.9808

0.0256

1.9629

\( 0.0348~\mbox{s} \)

1/256

π/16

1/16

0.0108

2.0100

0.0064

2.0000

\( 0.2327~\mbox{s} \)

1/1024

π/32

1/32

0.0027

2.0000

0.0016

2.0000

\( 14.0054~\mbox{s} \)

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