国家自然科学基金(61701518)
山东省“泰山学者"建设工程专项经费基金项目(20081130)
Appendix 显式渐近表达式的具体形式 式(A1)
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Figure 1
(Color online) Solution errors of PSWF $\mathrm{log}E_1$
Figure 2
(Color online) Solution errors of eigenvalues of differential operators of PSWF $\mathrm{log}E_2$
Figure 3
(Color online) The solution errors of PSWF
Figure 4
(Color online) The frequency domain energy concentration of PSWF
$c$ (rad$\cdot$s) | 11$\pi$ | 20$\pi$ | 40$\pi$ | 60$\pi$ | 80$\pi$ | 100$\pi$ | 101$\pi$ |
The values of the abscissas | 7.40 | 13.75 | 26.41 | 40.08 | 53.33 | 66.06 | 66.92 |
$c$ (rad$\cdot$s) | 11$\pi$ | 20$\pi$ | 40$\pi$ | 60$\pi$ | 80$\pi$ | 100$\pi$ | 101$\pi$ |
The values of the abscissas | 7.32 | 13.17 | 26.02 | 39.54 | 53.31 | 65.98 | 66.15 |
Method | Order | The 0th$\sim$13th PSWF | The 14th$\sim$19th PSWF |
This paper | The 0th$\sim$13th PSWF | $2.56~\times~10^{-32}~\sim~7.44~\times~10^{-15}$ | $5.14~\times~10^{-9}~\sim~8.08~\times~10^{-3}$ |
Ref. | $2.56~\times~10^{-32}~\sim~7.44~\times~10^{-15}$ | $1.39~\times~10^{-3}~\sim~4.62~\times~10^{+2}$ | |
Ref. | $6.35~\times~10^{-2}~\sim~2.83~\times~10^{+2}$ | $3.76~\times~10^{-2}~\sim~4.90~\times~10^{+1}$ | |
This paper | The 14th$\sim$19th PSWF | Symmetry | $1.74~\times~10^{-34}~\sim~9.29~\times~10^{-19}$ |
Ref. | $7.52~\times~10^{-2}~\sim~5.07~\times~10^{+2}$ | ||
Ref. | $1.74~\times~10^{-34}~\sim~9.29~\times~10^{-19}$ |
Method | Order | The 0th$\sim$66th PSWF | The 67th$\sim$99th PSWF |
This paper | The 0th$\sim$66th PSWF | $1.07~\times~10^{-30}~\sim~7.66~\times~10^{-14}$ | $7.51~\times~10^{-7}~\sim~2.33\times~10^{-2}$ |
Ref. | $1.07\times~10^{-30}~\sim~7.66~\times~10^{-14}$ | $3.54~\times~10^{-2}~\sim~9.85\times~10^{+1}$ | |
Ref. | $5.43~\times~10^{-2}~\sim~1.24~\times~10^{+3}$ | $6.30~\times~10^{-1}~\sim~7.12~\times~10^{+2}$ | |
This paper | The 67th$\sim$99th PSWF | Symmetry | $4.35~\times~10^{-33}~\sim~5.48~\times~10^{-17}$ |
Ref. | $6.94~\times~10^{-2}~\sim~3.07~\times~10^{+2}$ | ||
Ref. | $4.35\times~10^{-33}~\sim~5.48~\times~10^{-17}$ |