skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Deconinck, Bernard"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; (, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)
    We implement the numerical unified transform method to solve the nonlinear Schrödinger equation on the half-line. For the so-called linearizable boundary conditions, the method solves the half-line problems with comparable complexity as the numerical inverse scattering transform solves whole-line problems. In particular, the method computes the solution at any x and t without spatial discretization or time stepping. Contour deformations based on the method of nonlinear steepest descent are used so that the method’s computational cost does not increase for large x , t and the method is more accurate as x , t increase. Our ideas also apply to some cases where the boundary conditions are not linearizable. 
    more » « less
    Full Text Available 
  2. ; ; (, IMA Journal of Numerical Analysis)
    null (Ed.)
    Abstract We implement the unified transform method of Fokas as a numerical method to solve linear evolution partial differential equations on the half-line. The method computes the solution at any $$x$$ and $$t$$ without spatial discretization or time stepping. With the help of contour deformations and oscillatory integration techniques, the method’s complexity does not increase for large $x,t$ and the method is more accurate as $x,t$ increase (absolute errors are smaller, relative errors are bounded). Our goal is to make no assumptions on the functional form of the initial or boundary functions beyond some decay and smoothness, while maintaining high accuracy in a large region of the $(x,t)$ plane. 
    more » « less
    Full Text Available 
  3. ; ; (, Physica D: Nonlinear Phenomena)
    Full Text Available 
  4. ; ; ; (, Wave Motion)
    null (Ed.)
    Full Text Available