Pii: S0168-9274(02)00112-5
نویسندگان
چکیده
We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schrödinger equation (NLS) initially accelerate self focusing but later arrest the collapse, resulting instead in focusing–defocusing oscillations. The modified equation of the semi-discrete NLS, which is the NLS with highorder anisotropic dispersion, captures the arrest of collapse but not the subsequent oscillations. Discretization effects in perturbed NLS equations are also discussed. 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
منابع مشابه
Pii: S0168-9274(02)00174-5
This paper deals with a shape preserving method of interpolating positive data at points of the plane in R2. We formulate a problem in order to define a positive interpolation variational spline in the Sobolev space H(Ω), where Ω is a non-empty bounded set ofR2, by minimizing the semi-norm of orderm, and we discrete such problem in a finite element space. An algorithm allows us to compute the r...
متن کاملPii: S0168-9274(02)00116-2
In recent years, a great deal of attention has been devoted to Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. The surge of interest was triggered by the pressing need for efficient numerical techniques for simulations of extremely large-scale dynamical systems arising from circuit simulation, structural dynamics, and microelectromechanical systems. In th...
متن کاملPii: S0168-9274(01)00134-9
A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of very smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is studied and a refined postprocessing technique is proposed. 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
متن کاملPii: S0168-9274(99)00020-3
We compare several methods for sensitivity analysis of differential–algebraic equations (DAEs). Computational complexity, efficiency and numerical conditioning issues are discussed. Numerical results for a chemical kinetics problem arising in model reduction are presented. 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
متن کاملPii: S0168-9274(00)00050-7
The aim of this work is to present a nonstandard linear finite element method for a planar elasticity problem. The error for the solution computed with this method is estimated with respect to H 1 ×H 1-norm and second-order convergence is shown. 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
متن کامل