Haidvogel, Dale B.; Zang, Thomas The accurate solution of Poisson’s equation by expansion in Chebyshev polynomials. (English) Zbl 0397.65077 J. Comput. Phys. 30, 167-180 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 96 Documents MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35C10 Series solutions to PDEs 65F05 Direct numerical methods for linear systems and matrix inversion Keywords:Matrix Diagonalization; Dirichlet Boundary Conditions; Chebyshev Expansion; Alternating Direction PDF BibTeX XML Cite \textit{D. B. Haidvogel} and \textit{T. Zang}, J. Comput. Phys. 30, 167--180 (1979; Zbl 0397.65077) Full Text: DOI References: [1] Dorr, F.W., SIAM rev., 12, 248-263, (1970) [2] Swarztrauber, P.N., SIAM rev., 19, 490-501, (1977) [3] Isaacson, E.; Keller, H.B., Analysis of numerical methods, (1966), Wiley New York · Zbl 0168.13101 [4] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and application, (1977), Society for Industrial and Applied Mathematics Philadelphia [5] Orszag, S.A., J. fluid mech., 50, 689-703, (1971) [6] Lanczos, C., Applied analysis, (1956), Prentice-Hall Englewood Cliffs, N.J · Zbl 0111.12403 [7] Cooley, J.W.; Tukey, J.W., Math. comp., 19, 297-301, (1965) [8] Peaceman, D.W.; Rachford, H.H., SIAM j., 3, 28-41, (1955) [9] Haidvogel, D.B., Quasigeostrophic regional and general circulation modelling: an efficient pseudospectral approximation technique, () · Zbl 0551.76017 [10] Varga, R.S., Matrix iterative analysis, (1962), Prentice-Hall Englewood Cliffs, N.J · Zbl 0133.08602 [11] Wachspress, E.L., J. soc. indust. appl. math., 10, 339-350, (1962) [12] Murdock, J.W., Aiaa j., 15, 1167-1173, (1977) [13] \scD. B. Haidvogel, E. E. Schulman, and A. R. Robinson, to appear in Rept. Meteorol. Oceanogr. [14] Klema, V.K.; Garbow, B.S.; Moler, C.B., EISPACK, User’s information, (1973), Argonne National Laboratory, Applied Mathematics Division [15] Wilkinson, J.H., The algebraic eigenvalue problem, (1965), Clarendon Oxford · Zbl 0258.65037 [16] Bartels, R.H.; Stewart, G.W., Comm. ACM, 15, 820-826, (1972) [17] Swarztrauber, P.N.; Sweet, R.A., Efficient FORTRAN subprograms for the solution of elliptic partial differential equations, NCAR technical note, NCAR-TN/IA-109, (1975) [18] Pereyra, V., SIAM J. numer. anal., 4, 508-533, (1967) [19] Houstis, E.N.; Papatheodorou, T.S., Comparison of fast direct methods for elliptic problems, () · Zbl 0432.65054 [20] Lehman, R.S., J. math. mech., 8, 727-760, (1959) [21] Concus, P.; Golub, G.H., SIAM J. numer. anal., 10, 1103-1120, (1973) [22] Orszag, S.A., Stud. appl. math., 50, 293-327, (1971) [23] Sköllermo, G., Math. comp., 29, 697-711, (1975) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.