[1] Haltiner G J, Williams R T. Numerical prediction and dynamical meteorology [M]. NewYork: Wiley, 1980.[2] Williamson D L, Drake J B, Hack J J, et al. A standard test set for numerical approximationsto the shallow water equations in spherical geometry [J]. Journal of Computational Physics. 1992,102: 211-224.[3] Cao W M, Guo B Y. A pseudospectral method for vorticity equations on spherical surface [J].Acta Mathematicae Applicatae Sinica: English Series, 1997, 13(2): 176-187.[4] Guo B Y. A spectral method for vorticity equations on spherical surface [J]. Applied Mathematicsand Computation, 1995, 64: 1067-1079.[5] Guo B Y, Cao W M. A spectral method for the fluid flow with low Mach number on sphericalsurface [J]. Journal on Numerical Analysis, 1995, 32: 1764-1777.[6] Guo B Y, Wang L L. Jacobi interpolation approximations and their applications to singulardifferential equations [J]. Advances in Computational Mathematics, 2001, 14: 227-276.[7] Guo B Y. Jacobi approximations in certain Hilbert spaces and their applications to singulardifferential equations [J]. Journal of Mathematical Analysis and Applications, 2000, 243(2):373-408.[8] Guo B Y, Wang L L. Jacobi interpolation approximations in non-uniformly Jacobi-weightedSobolev spaces [J]. Journal of Approximation Theory, 2004, 128(1): 1-41.[9] 夏文杰, 黄伟. 求解Fisher 型方程的混合Legendre-球面调和谱方法[J]. 应用数学与计算数学学报,2014, 28(1): 26-32.[10] Bernardi C, Maday Y. Handbook of numerical analysis: spectral methods [J]. Techniques ofScientific Computing, 1997, 5: 209-485.[11] Guo B Y, Huang W. Mixed Jacobi-spherical harmonic spectral method for Navier-Stokes equations[J]. Applied Numerical Mathematics, 2007, 57: 939-961.[12] 黄伟, 郭本瑜. Navier-Stokes 方程的全离散Jacobi-球面调和谱方法[J]. 应用数学和力学, 2008,29(4): 409-431. |