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The accurate solution of Poisson’s equation by expansion in Chebyshev polynomials. (English) Zbl 0397.65077


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
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[1] Dorr, F. W., SIAM Rev., 12, 248-263 (1970) · Zbl 0208.42403
[2] Swarztrauber, P. N., SIAM Rev., 19, 490-501 (1977) · Zbl 0358.65088
[3] Isaacson, E.; Keller, H. B., Analysis of Numerical Methods (1966), Wiley: 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: Society for Industrial and Applied Mathematics Philadelphia · Zbl 0412.65058
[5] Orszag, S. A., J. Fluid Mech., 50, 689-703 (1971) · Zbl 0237.76027
[6] Lanczos, C., Applied Analysis (1956), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0111.12403
[7] Cooley, J. W.; Tukey, J. W., Math. Comp., 19, 297-301 (1965) · Zbl 0127.09002
[8] Peaceman, D. W.; Rachford, H. H., SIAM J., 3, 28-41 (1955) · Zbl 0067.35801
[9] Haidvogel, D. B., Quasigeostrophic regional and general circulation modelling: an efficient pseudospectral approximation technique, (Shaw, R. P., Computing Methods in Geophysical Mechanics, Vol. 25 (1977), American Society of Mechanical Engineers) · Zbl 0551.76017
[10] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0133.08602
[11] Wachspress, E. L., J. Soc. Indust. Appl. Math., 10, 339-350 (1962) · Zbl 0111.31401
[12] Murdock, J. W., AIAA J., 15, 1167-1173 (1977)
[13] D. B. Haidvogel, E. E. Schulman, and A. R. RobinsonRept. Meteorol. Oceanogr.; D. B. Haidvogel, E. E. Schulman, and A. R. RobinsonRept. 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: Clarendon Oxford · Zbl 0258.65037
[16] Bartels, R. H.; Stewart, G. W., Comm. ACM, 15, 820-826 (1972) · Zbl 1372.65121
[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) · Zbl 0265.65043
[19] Houstis, E. N.; Papatheodorou, T. S., Comparison of fast direct methods for elliptic problems, (Vichnevetsky, R., Advances in Computer Methods for Partial Differential Equations—II (1977), IMACS (AICA): IMACS (AICA) Brussels) · Zbl 0432.65054
[20] Lehman, R. S., J. Math. Mech., 8, 727-760 (1959) · Zbl 0094.29702
[21] Concus, P.; Golub, G. H., SIAM J. Numer. Anal., 10, 1103-1120 (1973) · Zbl 0245.65043
[22] Orszag, S. A., Stud. Appl. Math., 50, 293-327 (1971) · Zbl 0237.76012
[23] Sköllermo, G., Math. Comp., 29, 697-711 (1975) · Zbl 0317.65031
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