Theory and Modern Applications
Table 1 Maximum absolute errors of problem ( 63 )
N = M | \(\boldsymbol{\alpha }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{0}\) | \(\boldsymbol{\alpha }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\frac{1}{2}}\) | \(\boldsymbol{\alpha }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\frac{1}{2}}\) , \(\boldsymbol{\alpha }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta }_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{-\frac{1}{2}}\) | |||
|---|---|---|---|---|---|---|
\(\boldsymbol{M}_{\boldsymbol{1}}\) | \(\boldsymbol{M}_{\boldsymbol{2}}\) | \(\boldsymbol{M}_{\boldsymbol{1}}\) | \(\boldsymbol{M}_{\boldsymbol{2}}\) | \(\boldsymbol{M}_{\boldsymbol{1}}\) | \(\boldsymbol{M}_{\boldsymbol{2}}\) | |
4 | 1.54 × 10−2 | 1.98 × 10−2 | 2.33 × 10−2 | 2.92 × 10−2 | 2.29 × 10−2 | 2.88 × 10−2 |
8 | 8.04 × 10−7 | 1.07 × 10−6 | 1.50 × 10−6 | 1.98 × 10−6 | 1.50 × 10−6 | 2.01 × 10−6 |
12 | 5.15 × 10−12 | 6.88 × 10−12 | 1.12 × 10−11 | 1.51 × 10−11 | 1.13 × 10−11 | 1.46 × 10−11 |
16 | 8.55 × 10−15 | 9.33 × 10−15 | 4.61 × 10−15 | 4.33 × 10−15 | 5.44 × 10−15 | 5.77 × 10−15 |
20 | 6.66 × 10−15 | 7.55 × 10−15 | 3.11 × 10−15 | 3.33 × 10−15 | 3.11 × 10−15 | 3.00 × 10−15 |