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Numerical solutions of the regularized long-wave equation. (English) Zbl 0409.73012


MSC:

74J10 Bulk waves in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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References:

[1] Peregrine, D. H., Calculations of the development of an undular bore, J. Fluid Mech., 25, 321-330 (1966)
[2] Benjamin, T. B.; Bona, J. L.; Mahony, J. J., Model equations for long waves in nonlinear dispersive systems, Phil. Trans. Roy. Soc. London, 272A, 47-78 (1972) · Zbl 0229.35013
[3] Bona, J. L.; Bryant, P. J., A mathematical model for long waves generated by wavemakers in non-linear dispersive systems, (Proc. Cambridge Phil. Soc., 73 (1973)), 391-405 · Zbl 0261.76007
[4] Eilbeck, J. C.; McGuire, G. R., Numerical study of the regularized long-wave equation 1 : Numerical methods, J. Comp. Phys., 19, 43-57 (1975) · Zbl 0325.65054
[5] Eilbeck, J. C., Numerical studies of solitons, (Proceedings of a symposium on nonlinear structure and dynamics in condensed matter. Proceedings of a symposium on nonlinear structure and dynamics in condensed matter, Oxford, England, Jun. (1978), Springer: Springer Berlin), to appear. · Zbl 0644.65084
[6] Jain, P. C.; Iskandar, Labib; Kadalbajoo, M. K., Iterative techniques for non-linear boundary control problems, (Proceedings of International Conference on Optimization in Statistics (1979), Academic Press: Academic Press New York), 289-300
[7] Bellmann, R. E.; Kalaba, R. E., Quasilinearization and nonlinear boundary value problems (1965), American Elsevier: American Elsevier New York · Zbl 0139.10702
[8] Angel, E.; Bellmann, R., Dynamic programming and partial differential equations (1972), Academic Press: Academic Press New York
[9] Benjamin, T. B., The stability of solitary waves, (Proc. Roy. Soc. London, 328A (1972)), 153-182
[10] Kadalbajoo, M. K.; Jain, P. C., Invariant imbedding approach for the solution of the minimal surface equation, J. Math. Anal. Appl., 61, 643-657 (1977) · Zbl 0372.49018
[11] J.L. Bona, W.G. Pritchard and L.R. Scott (Univ. Essex Fluid Mechanics Research Institute, 1978).; J.L. Bona, W.G. Pritchard and L.R. Scott (Univ. Essex Fluid Mechanics Research Institute, 1978).
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