Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Errors and convergence orders of scheme (43)–(44) with an optimal step size ratio for τ, \(h_{1}\), \(h_{2}\) and Δβ (Example 1)

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

τ	\(h_{1}=h_{2}\)	Δβ	\(\\|e^{N} \\|_{L^{2}}\)	Order	\(\\|e^{N} \\|_{L^{\infty}}\)	Order	CPU time
1/64	π/2	1/8	0.7230	–	0.4602	–	0.0816 s
1/256	π/4	1/16	0.1689	2.0978	0.1195	1.9453	0.0483 s
1/1024	π/8	1/32	0.0426	1.9872	0.0301	1.9892	0.2603 s
1/4096	π/16	1/64	0.0107	1.9932	0.0075	2.0048	5.4613 s
1/16,384	π/32	1/128	0.0027	1.9866	0.0019	1.9809	166.2940 s
1/65,536	π/64	1/256	6.6801e−04	2.0150	4.7098e−04	2.0123	1 h 46 m 27 s

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