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Theory and Modern Applications

Table 2 Error estimates between the exact and regularized solutions for \(\tau = 1.7\), \(\alpha \in \{0.65, 0.75, 0.85, 0.95\}\)

From: Identification of source term for the ill-posed Rayleigh–Stokes problem by Tikhonov regularization method

 

ϵ

 

0.1

0.01

0.001

 

α = 0.65

\(\mathit{Err}^{\beta _{\mathrm{pri}}}\)

0.111131774567399

0.047840847429863

0.040796403046666

\(\mathit{Err}^{\beta _{\mathrm{pos}}}\)

0.104219494973211

0.047373969253811

0.040704667266564

 

α = 0.75

\(\mathit{Err}^{\beta _{\mathrm{pri}}}\)

0.042292184968334

0.032976631468816

0.025075858532616

\(\mathit{Err}^{\beta _{\mathrm{pos}}}\)

0.118817648652812

0.028123860184860

0.024430674882777

 

α = 0.85

\(\mathit{Err}^{\beta _{\mathrm{pri}}}\)

0.130527372052525

0.022400766773086

0.014919116713563

\(\mathit{Err}^{\beta _{\mathrm{pos}}}\)

0.082465125249822

0.020184320450563

0.014652593632991

 

α = 0.95

\(\mathit{Err}^{\beta _{\mathrm{pri}}}\)

0.045333767253358

0.011699213808191

0.008763429831879

\(\mathit{Err}^{\beta _{\mathrm{pos}}}\)

0.044277712631869

0.008651113194266

0.008905712655202