Homework Assignments: please hand in your homework during or at the end of my lecture in S14 #03-01 before its due date!! Late hand in will be deducted credits for the homework!!

• Homework 1 , Due date: 10:00pm February 16, 2009 (Monday).

• Homework 2 , Due date: 10:00pm March 16, 2009 (Monday).

• Homework 3: Please select one of the following papers, read the paper, do a presentation in the last two weeks in this semester and write a report. Due date of the report: 10:00pm April 27, 2009 (Monday).
  • B. K. Alpert and V. Rokhlin, A fast algorithm for the evalutation of Legendre expansions, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 158-179.
  • W. Bao, J. Shi and P. A. Markowich, On time-splitting spectral approximation for the Schrodinger equation in the semiclassical regime, J. Comput. Phys., 175 (2002), pp. 487-524. ---- ( Taken by Mr Zhang Wei )
  • W. Bao and J. Shen, A fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates, SIAM J. Sci. Comput., 26 (2005), pp. 2010-2028. ---- ( Taken by Mr Tang Qinglin )
  • W. S. Don and D. Gottlieb, The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points, SIAM J. Numer. Anal., 31 (1994), pp. 1519-1534. ---- ( Taken by Mr Shao Fang )
  • J. A. C. Weideman and L. N. Trefethen, The eigenvalues of second-order spectral differentiation matrices, SIAM J. Numer. Anal., 25 (1988), pp. 1279-1298. ---- ( Taken by Miss Abby Men )
  • J. Shen, Efficient spectral-Galerkin method II. direct solvers for second- and fourth-order equation by using Chebyshev polynomials, SIAM J. Sci. Comput., 16 (1995), pp. 74-87. ---- ( Taken by Miss Wang Xiaoyan )
  • J. Shen, Efficient spectral-Galerkin method III. polar and cylindrical geometries, SIAM J. Sci. Comput., 18 (1997), pp. 1583-1604. ---- ( Taken by Mr. Zhang Xiaowei )
  • D. Xiu and J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys., to appear.
  • L. Pareschi, G. Russo and G. Toscani, Fast spectral methods for the Fokker-Planck-Landau collision operator, J. Comput. Phys., 165 (2000), pp. 216-236. ---- ( Taken by Mr. Xu Weibiao )
  • C. Mouhot and L. Pareschi, Fast algorithms for computing the Boltzmann collision operator, Math. Comp. 75 (2006), pp. 1833-1852.
  • J. C. M. Fok, B.-Y. Guo and T. Tang, Combined Hermite spectral-finite difference method for the Fokker-Planck equations, Math. Comp., 71 (200), pp. 1497-1528.
  • B. Fornberg, A pseudospectral approach for polar and spherical geometries, SIAM J. Sci. Comput., 16 (1995), pp. 1071-1081.