Fairweather, G.; Navon, I. M. A linear ADI method for the shallow-water equations. (English) Zbl 0454.76032 J. Comput. Phys. 37, 1-18 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 76B99 Incompressible inviscid fluids 65Z05 Applications to the sciences Keywords:linear ADI method; shallow-water equations; potential enstrophy; alternating-direction implicit method PDF BibTeX XML Cite \textit{G. Fairweather} and \textit{I. M. Navon}, J. Comput. Phys. 37, 1--18 (1980; Zbl 0454.76032) Full Text: DOI References: [1] Gustafsson, B., J. Comput. Physics, 7, 239-254 (1971) [2] Orszag, S. A.; Israeli, M., Ann. Rev. Fluid Mech., 281-318 (1974) [3] Kwizak, M., Semi-implicit Integration of a Grid-Point Model of the Primitive Equations, (McGill University Publ. in Meteorology No. 98 (1970), Department of Meteorology) [4] Houghton, D.; Kasahara, A.; Washington, W., Mon. Weather Rev., 94, 141-150 (1966) [5] Douglas, J.; Gunn, J. E., Numer. Math., 6, 428-453 (1964) [6] Lees, M., (Ames, W. F., Nonlinear Partial Differential Equations (1967), Academic Press: Academic Press New York), 193-201 [7] Ahlberg, H. H.; Nilson, E. N.; Walsh, J. L., The Theory of Splines and Their Applications (1967), Academic Press: Academic Press New York · Zbl 0158.15901 [8] Yanenko, N. N., The Method of Fractional Steps (1971), Springer-Verlag: Springer-Verlag Berlin · Zbl 0209.47103 [9] Marchuk, G. I., Numerical Methods in Weather Prediction (1974), Academic Press: Academic Press New York [10] Hindmarsh, A. C., Solution of Block-Tridiagonal Systems of Linear Algebraic Equations, (UCID 30150 (1977), Lawrence Livermore Lab) · Zbl 0238.65020 [11] Grammeltvedt, A., Mon. Weather Rev., 97, No 5, 384-404 (1969) [12] Isaacson, E.; Keller, H. B., Analysis of Numerical Methods (1966), Wiley: Wiley New York · Zbl 0168.13101 [13] Navon, I. M., Algorithms for the Solution of Scalar and Block Cyclic Tridiagonal Systems, CSIR Special Report WISK 265 (1977), Pretoria, South Africa [14] Sadourny, R., J. Atmos. Sci., 32, 680-689 (1975) [15] Gary, J., Math. Comput., 18, 1-18 (1964) [16] Brissaud, A.; Frisch, U.; Leorat, J.; Lesieur, M.; Mazure, A.; Pouquet, A.; Sadourny, R.; Sulem, P. L., Ann. Geophys., 29, 539-546 (1973) [17] Navon, I. M., Beit. Phys. Atmos., 51, 281-305 (1978) [19] Bardos, C., (Nonlinear Partial Differential Equations. Nonlinear Partial Differential Equations, Lecture Notes in Mathematics No. 648 (1978), Springer-Verlag: Springer-Verlag New York), 1-46 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.