308
Views
3
CrossRef citations to date
0
Altmetric
Articles

A fast solution method for time dependent multidimensional Schrödinger equations

, &
Pages 408-429 | Received 16 Jul 2017, Accepted 21 Jul 2017, Published online: 08 Aug 2017

References

  • Evans LC . Partial differential equations. Vol. 19. Providence, RI: AMS; 2010.
  • Keel M , Tao T . Endpoint Strichartz estimates. Amer J Math. 1998;120:955–980.
  • Strichartz RS . Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations. Duke Math J. 1977;44:705–774.
  • Lanzara F , Maz’ya V , Schmidt G . On the fast computation of high dimensional volume potentials. Math Comput. 2011;80:887–904.
  • Lanzara F , Maz’ya V , Schmidt G . Accuracy cubature of volume potentials over high-dimensional half-spaces. J Math Sci. 2011;173:683–700.
  • Maz’ya V , Schmidt G . Approximate approximations. Vol. 141. Providence, RI: AMS; 2007.
  • Beylkin G , Mohlenkamp MJ . Numerical operator calculus in higher dimensions. Proc Nat Acad Sci USA. 2002;99:10246–10251.
  • Beylkin G , Mohlenkamp MJ . Algorithms for numerical analysis in high dimensions. SIAM J Sci Comput. 2005;26:2133–2159.
  • Lanzara F , Maz’ya V , Schmidt G . Fast cubature of volume potentials over rectangular domains by approximate approximations. Appl Comput Harmon Anal. 2014;36:167–182.
  • Lanzara F , Schmidt G . On the computation of high-dimensional potentials of advection- diffusion operators. Mathematika. 2015;61:309–327.
  • Lanzara F , Maz’ya V , Schmidt G . Approximation of solutions to multidimensional parabolic equations by approximate approximations. Appl Comput Harmon Anal. 2016;41:749–767.
  • Hestenes MR . Extension of the range of differentiable functions. Duke Math J. 1941;8:183–192.
  • Takahasi H , Mori M . Doubly exponential formulas for numerical integration. Publ RIMS, Kyoto Univ. 1974;9:721–741.
  • Abramowitz M , Stegun IA . Handbook of mathematical functions. New York (NY): Dover; 1968.
  • Arnold A , Schulte M . Transparent boundary conditions for quantum-waveguide simulations. Math Comput Simul. 2008;79:898–905.
  • Schulte M , Arnold A . Discrete transparent boundary conditions for the Schrödinger equation - a compact higher order scheme. Kinet Relat Model. 2008;1:101–125.

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.