Affordable Access

On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation

Authors
Publication Date
Disciplines
  • Law
  • Musicology
  • Physics

Abstract

On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation RAIRO MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE G. D. AKRIVIS V. A. DOUGALIS On a class of conservative, highly accurateGalerkin methods for the Schrödinger equation RAIRO – Modélisation mathématique et analyse numérique, tome 25, no 6 (1991), p. 643-670. <http://www.numdam.org/item?id=M2AN_1991__25_6_643_0> © AFCET, 1991, tous droits réservés. L’accès aux archives de la revue « RAIRO – Modélisation mathématique et analyse numérique » implique l’accord avec les conditions générales d’uti- lisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ l i / i > \ t l MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE (Vol. 25, n° 6, 1991, p. 643 à 670) ON A CLASS OF CONSERVATIVE, HIGHLY ACCURATE GALERKIN METHODS FOR THE SCHRÖDINGER EQUATION (*) G. D. AKRIVIS O and V. A. DOUGALIS O Communicated by J. BONA Dedicated to Professor Dr. G. Hâmmerlin on the occasion of his 60th birthday, July 31, 1988. Abstract. — We construct and analyze efficient fully discrete Galerkin type methods, that are of high order of accuracy and conservative in the L2 sense,for approximating the solution ofaform of the linear Schrödinger équation with a time-dependent coefficient, found e.g. in underwater acoustics. The time stepping procedures are based on the class of implicit Runge-Kutta methods known as the q-stage Gauss-Legendre schemes. L2 error estimâtes are proved that are of optimal order in space and of temporal order q + 2. An itérative procedure at each time step for the efficient implementation of the two-stage scheme is proposed and analyzed. Resumé. — On construit et analyse des méthodes totalement discrète

There are no comments yet on this publication. Be the first to share your thoughts.