Homework Assignments: please hand in your homework during or at the end of my lecture in S17 #08-18 before its due date!! Late hand in will be deducted credits for the homework!!

• Homework 1 , Due date: 6:00pm February 12, 2016 (Friday).
• Homework 2 , Due date: 6:00pm March 11, 2016(Friday).
• Homework 3 , Due date: 6:00pm April 1, 2016 (Friday).
• Project: Please select one of the following papers, read the paper, implement the algorithm in the paper, and do a presentation in the last two weeks in this semester and write a report. Due date of the report: 6:00pm (Friday).
  • 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. — ( Taken by Xavier CANTON and Zhu Changbo )
  • 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 Jia Yin and Teng Zhang )
  • 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 Taiying Jiang and Shuang Liu )
  • 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 Lilong Qian and Guojiang Xi )
  • 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 Loke Gar Goei and Chng Yuan Zhang Maurice )
  • 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 xxx )
  • J. Shen, Efficient spectral-Galerkin method III. polar and cylindrical geometries, SIAM J. Sci. Comput., 18 (1997), pp. 1583-1604. —- ( Taken by xxx )
  • 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 xxx )
  • C. Mouhot and L. Pareschi, Fast algorithms for computing the Boltzmann collision operator, Math. Comp. 75 (2006), pp. 1833-1852. —- ( Taken by Hanwen Cui and Zhenqian E )
  • 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.