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Table 1 Numerical results for Example 1 (\(\theta =0.5\), \(\sigma=1\), \(\lambda=5\), \(\alpha=0.5\))

From: A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation

nx(n)FMGAOMGM
\(\|u^{*}-\tilde{u}_{n}\|_{1}\)C.O.\(\|u^{*}-\tilde {u}_{n}\|_{2}\)C.O.\(\|u^{*}-u_{n}\|_{1}\)C.O.\(\|u^{*}-u_{n}\| _{2}\)C.O.
4154.3753e-2 8.8248e-4 4.3753e-2 8.8244e-4 
5312.1963e-20.99432.2097e-41.99772.1963e-20.99432.2089e-41.9982
6631.0992e-20.99865.5325e-51.99781.0992e-20.99865.5278e-51.9986
71275.4975e-30.99961.3886e-51.99435.4975e-30.99961.3867e-51.9950
82552.7489e-30.99993.4821e-61.99562.7489e-30.99993.4757e-61.9963
95111.3745e-31.00008.7666e-71.98991.3745e-31.00008.7453e-71.9907
1010236.8724e-31.00002.2071e-71.98996.8724e-31.00002.1997e-71.9912