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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A spectral method for the vorticity equation on the surface
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by Ben Yu Guo PDF
Math. Comp. 64 (1995), 1067-1079 Request permission


A spectral scheme is proposed for the vorticity equation defined on the spherical surface. Generalized stability and convergence are proved. The approximation results in this paper are also useful for other nonlinear problems.
  • James H. Bramble and Joseph E. Pasciak, A boundary parametric approximation to the linearized scalar potential magnetostatic field problem, Appl. Numer. Math. 1 (1985), no. 6, 493–514. MR 814774, DOI 10.1016/0168-9274(85)90034-0
  • Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang, Spectral methods in fluid dynamics, Springer Series in Computational Physics, Springer-Verlag, New York, 1988. MR 917480, DOI 10.1007/978-3-642-84108-8
  • R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • David Gottlieb and Steven A. Orszag, Numerical analysis of spectral methods: theory and applications, CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1977. MR 0520152, DOI 10.1137/1.9781611970425
  • Ben Yu Guo, Spectral method for solving Navier-Stokes equation, Sci. Sinica Ser. A 28 (1985), no. 11, 1139–1153. MR 828694
  • —, Difference method for partial differential equations, Science Press, Beijing, 1988.
  • Ben Yu Guo and He Ping Ma, Strict error estimation for a spectral method of compressible fluid flow, Calcolo 24 (1987), no. 3-4, 263–282 (1988). MR 1004522, DOI 10.1007/BF02679111
  • Ben Yu Guo, He Ping Ma, Wei Ming Cao, and Hui Huang, The Fourier-Chebyshev spectral method for solving two-dimensional unsteady vorticity equations, J. Comput. Phys. 101 (1992), no. 1, 207–217. MR 1173346, DOI 10.1016/0021-9991(92)90053-2
  • G. J. Haltiner, Numerical prediction, Wiley, New York, 1971. G. J. Haltiner and R. T. Williams, Numerical prediction and dynamical meteorology, Wiley, New York, 1980.
  • M. Jarraud and A. P. M. Baede, The use of spectral techniques in numerical weather prediction, Large-scale computations in fluid mechanics, Part 2 (La Jolla, Calif., 1983) Lectures in Appl. Math., vol. 22, Amer. Math. Soc., Providence, RI, 1985, pp. 1–41. MR 818778
  • Heinz-Otto Kreiss and Joseph Oliger, Stability of the Fourier method, SIAM J. Numer. Anal. 16 (1979), no. 3, 421–433. MR 530479, DOI 10.1137/0716035
  • Pen Yu Kuo, Error estimation for a spectral method of solving the KdV-Burgers equation, Shanghai Kexue Jishu Daxue Xuebao 2 (1983), 1–15 (Chinese, with English summary). MR 838695
  • J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. J. L. Lions and E. Magenes, Nonhomogeneous boundary value problems and applications, Vol. 1, Springer-Verlag, Berlin, 1972.
  • Y. Maday and A. Quarteroni, Spectral and pseudospectral aproximations of the Navier-Stokes equations, SIAM J. Numer. Anal. 19 (1982), no. 4, 761–780. MR 664883, DOI 10.1137/0719053
  • Joseph E. Pasciak, Spectral methods for a nonlinear initial value problem involving pseudodifferential operators, SIAM J. Numer. Anal. 19 (1982), no. 1, 142–154. MR 646600, DOI 10.1137/0719007
  • Robert D. Richtmyer and K. W. Morton, Difference methods for initial-value problems, 2nd ed., Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0220455
  • Qingcun Zen, Physical-mathematical basis of numerical prediction, Vol. 1, Science Press, Beijing, 1979.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1067-1079
  • MSC: Primary 65N35; Secondary 76D05, 76M25
  • DOI:
  • MathSciNet review: 1297463