Theory and Modern Applications
Table 5 Comparison based on relative errors for problem ( 70 )
N = M = K | \(\boldsymbol{\alpha}_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha}_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\alpha}_{\boldsymbol{3}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{3}}\boldsymbol{=}\boldsymbol{0}\) | N = M = K | \(\boldsymbol{\alpha}_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha}_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\alpha}_{\boldsymbol{3}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{3}}\boldsymbol{=}\boldsymbol{\frac{1}{2}}\) | ||||
|---|---|---|---|---|---|---|---|
\(\boldsymbol{R}^{\boldsymbol{u}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{v}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{\psi}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{u}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{v}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{\psi}}_{\boldsymbol{M}}\) | ||
4 | 5.06 × 10−5 | 2.88 × 10−5 | 3.65 × 10−5 | 4 | 6.32 × 10−5 | 4.07 × 10−5 | 4.84 × 10−5 |
6 | 1.14 × 10−7 | 4.76 × 10−8 | 7.36 × 10−8 | 6 | 1.70 × 10−7 | 8.88 × 10−8 | 1.19 × 10−7 |
8 | 1.15 × 10−10 | 3.70 × 10−11 | 6.85 × 10−11 | 8 | 2.00 × 10−10 | 9.04 × 10−11 | 1.32 × 10−10 |
N = M = K | \(\boldsymbol{\alpha}_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\alpha}_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\alpha}_{\boldsymbol{3}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{1}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{2}}\boldsymbol{=}\boldsymbol{\beta}_{\boldsymbol{3}}\boldsymbol{=}\boldsymbol{-\frac{1}{2}}\) | ( N , M , K ) | Symmetric Sinc-Galerkin method [ 39 ] | ||||
|---|---|---|---|---|---|---|---|
\(\boldsymbol{R}^{\boldsymbol{u}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{v}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{\psi}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{u}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{v}}_{\boldsymbol{M}}\) | \(\boldsymbol{R}^{\boldsymbol{\psi}}_{\boldsymbol{M}}\) | ||
4 | 3.38 × 10−5 | 1.34 × 10−5 | 2.15 × 10−5 | (8,8,1,000) | 1.56 × 10−5 | 1.40 × 10−5 | 2.30 × 10−5 |
6 | 6.03 × 10−8 | 2.41 × 10−8 | 3.36 × 10−8 | (16,16,1,000) | 4.51 × 10−7 | 5.04 × 10−7 | 6.77 × 10−7 |
8 | 4.84 × 10−11 | 3.51 × 10−11 | 3.05 × 10−11 | (32,32,1,000) | 2.98 × 10−9 | 4.90 × 10−9 | 5.62 × 10−9 |