Theory and Modern Applications
Table 2 Problem 6.1 : The maximum absolute errors
h | Proposed method ( 5.16 ) | Method discussed in [ 33 ] | ||||
|---|---|---|---|---|---|---|
\(\boldsymbol{\alpha_{0} = 12}\) , \(\boldsymbol{\beta_{0} = 8}\) , η = γ = 1 | \(\boldsymbol{\alpha_{0} = \beta_{0} = \pi}\) , η = 0.75, γ = 1.5 | \(\boldsymbol{\alpha_{0} = 3\pi}\) , \(\boldsymbol{\beta_{0} = \pi}\) , η = 2.5, γ = 0.25 | \(\boldsymbol{\alpha_{0} = 12}\) , \(\boldsymbol{\beta_{0} = 8}\) , η = γ = 1 | \(\boldsymbol{\alpha_{0} = \beta_{0} = \pi}\) , η = 0.75, γ = 1.5 | \(\boldsymbol{\alpha_{0} = 3\pi}\) , \(\boldsymbol{\beta_{0} = \pi}\) , η = 2.5, γ = 0.25 | |
1/16 | 7.4557(−07) | 2.0167(−06) | 1.6177(−06) | 5.6408(−06) | 4.4195(−06) | 1.1784(−06) |
1/32 | 5.7283(−08) | 1.2715(−07) | 1.0973(−07) | 6.6551(−07) | 5.4996(−07) | 1.5953(−07) |
1/64 | 3.6216(−09) | 7.9466(−09) | 6.8903(−09) | 7.2547(−08) | 6.4606(−08) | 2.0470(−08) |