260
Views
0
CrossRef citations to date
0
Altmetric
Articles

Why Magnus expansion

&
Pages 21-30 | Received 30 Jan 2021, Accepted 27 May 2021, Published online: 16 Jun 2021

References

  • A. Arnal, F. Casas and C. Chiralt, A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators, J. Phys. Commun. 2 (2018), p. 035024.
  • A. Arnal, F. Casas, C. Chiralt and J.A. Oteo, A unifying framework for perturbative exponential factorizations, Mathematics 9 (2021), p. 637.
  • C. Baumslag and B. Chandler (eds.), Wilhelm Magnus Collected Papers, Springer-Verlag, New York, 1984.
  • S. Blanes and F. Casas, A Concise Introduction to Geometric Numerical Integration, London: Chapman and Hall/CRC, 2016.
  • S. Blanes, F. Casas, J.A. Oteo and J. Ros, Magnus and Fer expansions for matrix differential equations: the convergence problem, J. Phys. A: Math. Gen. 22 (1998), pp. 259–268.
  • S. Blanes, F. Casas, J.A. Oteo and J. Ros, The Magnus expansion and some of its applications, Phys. Rep. 470 (2009), pp. 151–238.
  • A. Erdélyi, W. Magnus, F. Oberhettinger and F. Tricomi, Higher Transcendental Functions I, II and III, McGraw Hill, New York. Vols. I and II, 1953, Vol. III, 1955. The whole set was reprinted in 1981 by Krieger, Melbourne, Florida.
  • A. Erdélyi, W. Magnus, F. Oberhettinger and F. Tricomi, Tables of Integral Transforms, 2 Vols. McGraw Hill, New York, 1954.
  • E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed., Springer, 2006.
  • A. Iserles and S.P. Nørsett, On the solution of linear differential equations in Lie groups, Phil. Trans. R. Soc. A 357 (1999), pp. 983–1019. Theme Issue ‘Geometric integration: numerical solution of differential equations on manifolds’, compiled by C.J. Budd and A. Iserles.
  • S. Klarsfeld, Padé approximants and multiphoton ionisation of atomic hydrogen, J. Phys. B: Atom. Mol. Phys. 12 (1979), pp. L553–L556.
  • S. Klarsfeld, Padé approximants and related methods for computing boundary values on cuts, in Padé Approximation and Its Applications, Lecture Notes in Mathematics, Vol. 888, pp. 255–262, Springer, Berlin, 1981.
  • S. Klarsfeld, J. Martorell, J.A. Oteo, M. Nishimura and D.W.L. Sprung, Determination of the deuteron mean square radius, Nucl. Phys. A 456 (1986), pp. 373–396.
  • S.L. Segal, Mathematicians under the Nazis, Princeton: Princeton University Press, 2005.
  • R. Siegmund-Schultze, Rockefeller and the Internationalization of Mathematics between the two World Wars, Berlin: Springer Basel AG, 2001.
  • W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. VII (1954), pp. 649–673. Reprinted in [3] pp. 423–447.
  • W. Magnus, Vignette of a cultural episode, in Studies in Numerical Analysis, B.K. Scaife, ed., Academic Press, London, 1974, pp. 7–13. Reprinted in [3] pp. 623–629.
  • P.C. Moan, Efficient approximation of Sturm-Liouville problems using lie-group methods, Technical Report 1998/NA11, DAMTP, University of Cambridge, Cambridge UK, 1998.
  • P.C. Moan and J. Niesen, Convergence of the Magnus series, Found. Comput. Math 8 (2008), pp. 291–301.
  • D.W. Robinson, Multiple Coulomb excitations of deformed nuclei, Helv. Phys. Acta 36 (1963), pp. 140–154.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.