國家理論科學研究中心數學組 & 靜宜大學應用數學系

2005 春季專題課程

 High-order Methods for PDEs and Related Topics

偏微分方程之高階數值方法及相關課題

< Second Announcement >

(1)

Speaker  :  林吉田 教授(靜宜大學)

Time       :   February 24 & March 3, 10, 17, 2005     9:00-12:00

Title        :   Finite difference methods for conservation laws.

1. Derivation of Euler system.

2. Conservative schemes, consistency, stability and convergence.

3. Numerical dissipation, numerical dispersion and group speed.

4. Riemann problems and field decomposition.

5. TVD schemes.

6. Central schemes.

7. Central-upwind schemes.

8. Semidiscrete central-upwind schemes.

Reference: LeVeque: Numerical Methods for Conservation Laws
                Papers by Nessyahu, Tadmor, Kurganov, Lin, Levy, et al.

(2)

Speaker  :  郭本瑜 教授(上海師範大學)

Time       :   March 24, 31 & April 7, 14, 2005     9:00-12:00

Title        :   Spectral methods for PDEs on bounded or unbounded domains.

1. Jacobi approximations and Jacobi spectral methods.

2. Spectral method on triangle.

3. Hermite spectral method.

4. Laguerre spectral method.

5. Mixed Laguerre spectral-spherical harmonic method for the whole space.

6. Mixed Laguerre spectral-spherical harmonic method for exterior problems.

7. Domain decomposition spectral method for unbouded problems.

8. Rational spectral method.

9. Spectral-projection method for Naver-stokes equations.

Reference:  LeVeque: Numerical Methods for Conservation Laws
                  Papers by Nessyahu, Tadmor, Kurganov, Lin, Levy, et al.

Place       : 靜宜大學應用數學系第一研究大樓101室