Werner Liniger

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Werner Liniger (born December 22, 1927 in Tschugg near Bern ) is an American mathematician of Swiss origin.

Liniger studied mathematics at the ETH Zurich (diploma in 1951) and received his doctorate in 1956 from the University of Lausanne with a thesis on the stability of numerical integration methods ( dr ès sc. ). In 1957 he emigrated to the USA . After two years in the Univac Division of the Sperry Rand Corporation in Philadelphia, he moved to the IBM Research Center in Yorktown Heights in 1959 . There he was a staff member in the Mathematical Sciences Department . In 1993, Liniger retired. From 1972 to 1973 he was visiting professor at EPFL and the University of Neuchâtel .

Liniger's main area of ​​interest was numerical analysis , in particular the development and analysis of numerical methods for the integration of ordinary differential equations . The method developed together with Ralph A. Willoughby for the efficient solution of “stiff” differential equations has found its way into numerics textbooks. Liniger also explored applications of his methods to problems in physics, materials science, and biology.

Together with Elliott Lieb he wrote a fundamental work on the Bose-Einstein condensation of interacting systems ("Lieb-Liniger model"). Consider a system of bosonic particles in a dimension that a repulsive -shaped interact potential. The model represents a generalization of the Girardeau model of impenetrable bosons (hardcore bosons) . Lieb and Liniger were able to determine the eigenfunctions of the model exactly with the Bethe approach and show that in the limiting case of weak coupling, Bogoliubov's perturbation theory is correct. In the 2000s it was shown that the model provides a good description of the ground state and low excitations of a Bose gas in a (three-dimensional) long cylinder.

Liniger is a member of the Society for Industrial and Applied Mathematics , the Association for Computing Machinery, and the Society for Applied Mathematics and Mechanics .

He lives in Victor, New York .

Fonts (selection)

  • EH Lieb, W. Liniger: Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State . In: Physical Review . tape 130 , 1963, pp. 1605-1616 , doi : 10.1103 / PhysRev.130.1605 .
  • W. Liniger, RA Willoughby: Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations . In: SIAM J. Numer. Anal. tape 7 , no. 1 , 1970, p. 47-66 , doi : 10.1137 / 0707002 .
  • FG Gustavson, W. Liniger, R. Willoughby: Symbolic Generation of an Optimal Crout Algorithm for Sparse Systems of Linear Equations . In: Journal of the ACM . tape 17 , no. 1 , 1970, p. 87-109 .
  • W. Liniger, F. Odeh: A-stable, Accurate Averaging of Multistep Methods for Stiff Differential Equations . In: IBM Journal of Research and Development . tape 16 , no. 4 , 1972, p. 335-348 , doi : 10.1147 / around 164.0335 .
  • O. Nevanlinna, W. Liniger: contractive methods for stiff differential equations part I . In: BIT Numerical Mathematics . tape 18 , no. 4 , 1978, p. 457-474 , doi : 10.1007 / BF01932025 .
  • W. Liniger, F. Odeh, V. Hara: A second-order sparse factorization method for Poisson's equation with mixed boundary conditions . In: Journal of Computational and Applied Mathematics . tape 44 , no. 2 , December 17, 1992, p. 201-218 , doi : 10.1016 / 0377-0427 (92) 90011-L .
  • AE Ruehli, W. Liniger, P. Pattnaik: Integrators for stiff systems with undamped oscillatory solutions . In: Numerical Functional Analysis and Optimization . tape 16 , no. 3-4 , 1995, pp. 531-545 , doi : 10.1080 / 01630569508816630 .
  • US patent: Parallel computation of the response of a physical system . US5629845A. August 17, 1995 ( google.com ).

Web links

  • Short biography of the authors (with picture) in: W. Liniger: Multistep and one-leg methods for implicit mixed differential algebraic systems . In: IEEE Transactions on Circuits and Systems . tape 26 , no. 9 , 1979, pp. 755-762 ( ieee.org ).
  • Werner Liniger. In: dblp computer science bibliography.
  • List of publications and citations. Scopus;

Individual evidence

  1. ↑ Liniger, Werner: On the stability of numerical integration methods for differential equations . Dissertation University of Lausanne. L. Speich, Zurich 1957.
  2. ↑ a b Authors . In: IBM Res. Develop. tape 16 , no. 4 , July 1972, p. 446 ( ieee.org ).
  3. ^ Change of Address for Werner Liniger. May 12, 1993. Retrieved November 1, 2018 .
  4. ↑ Werner Liniger, Ralph A. Willoughby: Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations . In: SIAM J. Numer. Anal. tape 7 , no. 1 , p. 47-66 , doi : 10.1137 / 0707002 .
  5. ↑ Rolf Dieter Grigorieff: Numerics of ordinary differential equations 2nd multi-step method . Vieweg + Teubner Verlag, 1977, ISBN 978-3-519-02045-5 , Chapter 3.4 , doi : 10.1007 / 978-3-322-91202-2 .
  6. ^ G. Wanner: On the integration of stiff differential equations . In: Descloux J., Marti J. (Eds.): Numerical Analysis. International Series of Numerical Mathematics . tape 37 . Birkhäuser, Basel 1977, ISBN 978-3-0348-5575-4 , pp. 209–226 , doi : 10.1007 / 978-3-0348-5575-4_11 ( springer.com [PDF]).
  7. ^ W. Liniger: On the proximity effect in a superconductive slab bordered by metal . In: J Low Temp Phys . tape 93 , no. 1 , 1993, p. 1-6 , doi : 10.1007 / BF00682277 .
  8. ^ MD Thouless, W. Liniger: Effects of surface and boundary diffusion on void growth . In: Acta Metallurgica et Materialia . tape 43 , no. 6 , 1995, pp. 2493-2500 , doi : 10.1016 / 0956-7151 (94) 00411-0 .
  9. ^ W. Liniger, G. Karreman, R. Rawala, R. Colman: Mathematical model of the activation of prothrombin by factor X a and factor V t . In: Bulletin of Mathematical Biology . tape 42 , 1980, pp. 861 , doi : 10.1007 / BF02461064 .
  10. ↑ Elliott H. Lieb: Lieb-Liniger model of a Bose Gas . In: Scholarpedia . tape 3 , no. 12 , 2008, p. 8712 , doi : 10.4249 / scholarpedia.8712 .
  11. ↑ Werner M Liniger. In: whitepages.com. Retrieved November 1, 2018 .
personal data
SURNAME Liniger, Werner
BRIEF DESCRIPTION American mathematician of Swiss origin
DATE OF BIRTH December 22, 1927
PLACE OF BIRTH Tschugg near Bern