Numerische Mathematik

, Volume 68, Issue 3, pp 355–376

Orthogonal spline collocation methods for Schr\"{o}dinger-type equations in one space variable

  • Mark P. Robinson
  • Graeme Fairweather

DOI: 10.1007/s002110050067

Cite this article as:
Robinson, M. & Fairweather, G. Numer. Math. (1994) 68: 355. doi:10.1007/s002110050067

Summary.

We examine the use of orthogonal spline collocation for the semi-discreti\-za\-tion of the cubic Schr\"{o}dinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order\(L^2\) estimate of the error in the semidiscrete approximation is derived. For the cubic Schr\"{o}dinger equation, we present the results of numerical experiments in which the integration in time is performed using a routine from a software library.

Mathematics Subject Classification (1991): 65M15, 65M20, 65M70 

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Mark P. Robinson
    • 1
  • Graeme Fairweather
    • 2
  1. 1.Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA US
  2. 2.Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA US

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