|
Online ISSN 1552-4485; Print ISSN 0033-569X
The beginnings of applied mathematics after the Second World War
Author:
Peter D. Lax
Journal:
Quart. Appl. Math. 56 (1998), 607-615
MSC:
Primary 01A60
DOI:
https://doi.org/10.1090/qam/1668731
MathSciNet review:
MR1668731
Full-text PDF Free Access
References | Similar Articles | Additional Information
-
H. Cramér, Études sur la sommation des series de Fourier, Arkiv för Matematik 13, #20 (1919)
- P. Deift and K. T-R McLaughlin, A continuum limit of the Toda lattice, Mem. Amer. Math. Soc. 131 (1998), no. 624, x+216. MR 1407901, DOI https://doi.org/10.1090/memo/0624
- H. Flaschka, On the Toda lattice. II. Inverse-scattering solution, Progr. Theoret. Phys. 51 (1974), 703–716. MR 408648, DOI https://doi.org/10.1143/PTP.51.703
- Alan C. Newell (ed.), Nonlinear wave motion, American Mathematical Society, Providence, R.I., 1974. Lectures in Applied Mathematics, Vol. 15. MR 0336014
- Jonathan Goodman and Peter D. Lax, On dispersive difference schemes. I, Comm. Pure Appl. Math. 41 (1988), no. 5, 591–613. MR 948073, DOI https://doi.org/10.1002/cpa.3160410506
- David Gottlieb and Chi-Wang Shu, On the Gibbs phenomenon and its resolution, SIAM Rev. 39 (1997), no. 4, 644–668. MR 1491051, DOI https://doi.org/10.1137/S0036144596301390
- Brian T. Hayes, Binary modulated oscillations in a semi-discrete version of Burgers equation, Phys. D 106 (1997), no. 3-4, 287–313. MR 1462316, DOI https://doi.org/10.1016/S0167-2789%2897%2900044-4 B. L. Holian and G. K. Straub, Molecular dynamics of shock waves in one-dimensional chains, Phys. Rev. B 18, 1593–1608 (1978)
- Brad Lee Holian, Hermann Flaschka, and David W. McLaughlin, Shock waves in the Toda lattice: analysis, Phys. Rev. A (3) 24 (1981), no. 5, 2595–2623. MR 635742, DOI https://doi.org/10.1103/PhysRevA.24.2595
- Thomas Y. Hou and Peter D. Lax, Dispersive approximations in fluid dynamics, Comm. Pure Appl. Math. 44 (1991), no. 1, 1–40. MR 1077912, DOI https://doi.org/10.1002/cpa.3160440102
- Spyridon Kamvissis, On the Toda shock problem, Phys. D 65 (1993), no. 3, 242–266. MR 1222811, DOI https://doi.org/10.1016/0167-2789%2893%2990161-S
- Peter D. Lax, On dispersive difference schemes, Phys. D 18 (1986), no. 1-3, 250–254. Solitons and coherent structures (Santa Barbara, Calif., 1985). MR 838330, DOI https://doi.org/10.1016/0167-2789%2886%2990185-5
- Peter Lax and Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217–237. MR 120774, DOI https://doi.org/10.1002/cpa.3160130205 P. D. Lax and D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, Comm. Pure Appl. Math., I: pp. 253–290, II: pp. 571–593, III: pp. 160–169 (1983)
- C. David Levermore and Jian-Guo Liu, Large oscillations arising in a dispersive numerical scheme, Phys. D 99 (1996), no. 2-3, 191–216. MR 1439458, DOI https://doi.org/10.1016/S0167-2789%2896%2900157-1 J. von Neumann, Proposal and analysis of a new numerical method in the treatment of hydrodynamical shock problems, Collected Works, vol. 6, Pergamon Press, London, 1963 J. von Neumann and H. H. Goldstine, On the principles of large scale computing machines, Collected Works, vol. 5, Pergamon Press, London, 1963
- J. Von Neumann and R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks, J. Appl. Phys. 21 (1950), 232–237. MR 37613
- Cristina Vilma Turner and Rodolfo Rubén Rosales, The small dispersion limit for a nonlinear semidiscrete system of equations, Stud. Appl. Math. 99 (1997), no. 3, 205–254. MR 1468971, DOI https://doi.org/10.1111/1467-9590.00060 O. Szász, Gibbs phenomenon for Hausdorff means, Trans. Amer. Math. Soc. 69, 1077–1093 (1950)
- Morikazu Toda, Nonlinear lattice dynamics, Iwanami Shoten, Tokyo, 1978 (Japanese). MR 601779 J. G. Trulio and K. R. Trigger, Numerical Solution of One Dimensional Hydrodynamical Shock Problems, UCRL Report 6522, 1961
- Stephanos Venakides, Percy Deift, and Roger Oba, The Toda shock problem, Comm. Pure Appl. Math. 44 (1991), no. 8-9, 1171–1242. MR 1127056, DOI https://doi.org/10.1002/cpa.3160440823 A. Zygmund, Trigonometric Series, second edition, Cambridge University Press, Cambridge, 1959
Retrieve articles in Quarterly of Applied Mathematics with MSC: 01A60
Retrieve articles in all journals with MSC: 01A60
Additional Information
Article copyright:
© Copyright 1998
American Mathematical Society