Christie, I.; Sanz-Serna, J. M. A Galerkin method for a nonlinear integro-differential wave system. (English) Zbl 0525.73089 Comput. Methods Appl. Mech. Eng. 44, 229-237 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 14 Documents MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 74H45 Vibrations in dynamical problems in solid mechanics 74K05 Strings 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74S99 Numerical and other methods in solid mechanics Keywords:Galerkin method; vibrations of string; increase in tension; convergence of semidiscrete approximations; numerical tests; wave equation; nonlinear integro-differential equation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Antman, S. S., The equations for large vibrations of strings, Amer. Math. Monthly, 87, 359-370 (1980) · Zbl 0435.73056 [2] Dickey, R. W., Infinite systems of nonlinear oscillation equations related to the string, (Proc. Amer. Math. Soc., 23 (1969)), 459-468 · Zbl 0218.34015 [3] Woinowsky-Krieger, S., The effect of axial forces on the vibrations of hinged bars, J. Appl. Mech., 17, 35-36 (1980) · Zbl 0036.13302 [4] Eisley, J. G., Nonlinear vibrations of beams and rectangular plates, Z. Angew. Math. Phys., 15, 167-175 (1964) · Zbl 0133.19101 [5] Dupont, T., Galerkin methods for first order hyperbolics: an example, SIAM J. Numer. Anal., 10, 890-899 (1973) · Zbl 0237.65070 [6] Pen-Yu, Kuo; Sanz-Serna, J. M., Convergence of methods for the numerical solution of the Korteweg-de Vries equation, IMA J. Numer. Anal., 1, 215-221 (1981) · Zbl 0455.65082 [7] Lambert, J. D., Computational Methods in Ordinary Differential Equations (1973), Wiley: Wiley New York · Zbl 0258.65069 [8] Griffiths, D. F.; Mitchell, A. R.; Morris, J. Ll., A numerical study of the nonlinear Schroedinger equation, Comput. Meths. Appl. Mech. Engrg., 45 (1984) · Zbl 0555.65060 [9] Sanz-Serna, J. M., An explicit finite difference scheme with exact conservation properties, J. Comput. Phys., 47, 199-210 (1982) · Zbl 0484.65062 [10] Sanz-Serna, J. M.; Manoranjan, V. S., A method for the integration in time of certain partial differential equations, J. Comput. Phys., 52, 273-289 (1983) · Zbl 0514.65085 [11] Sanz-Serna, J. M., Methods for the numerical solution of the nonlinear Schröedinger equation, Math. Comp., 43 (1984), to appear. · Zbl 0555.65061 [12] Delfour, M.; Fortin, M.; Payne, G., Finite difference solution of a nonlinear Schröedinger equation, J. Comput. Phys., 44, 277-288 (1981) · Zbl 0477.65086 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.