Complex Valued Spectral Hermite Approximations for the Actively Mode-Locked Laser

Authors:
Kelly Black;John B. Geddes
Affiliations:
Department of Mathematics, Union College, Schenectady, USA;Franklin W. Olin College of Engineering, Needham, USA
Venue:
Journal of Scientific Computing
Year:
2007

Citing 8
Cited 1

Orthogonal rational functions on a semi-infinite interval

Journal of Computational Physics
Spectral methods and mappings for evolution equations on the infinite line

ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Spectral Elements on Infinite Domain

SIAM Journal on Scientific Computing
Error estimation of Hermite spectral method for nonlinear partial differential equations

Mathematics of Computation
Spectral Hermite Approximations for the Actively Mode-Locked Laser

Journal of Scientific Computing
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions

SIAM Journal on Numerical Analysis
The fast Gauss transform with complex parameters

Journal of Computational Physics
A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates

SIAM Journal on Scientific Computing

Noise-induced oscillations in an actively mode-locked laser

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We construct a numerical approximation of the governing equations of an actively mode-locked laser. The governing equation is complex valued and a novel scaling is employed that is designed to simplify the associated line integral in the complex plane. The resulting approximation is based on a set of shifted Hermite polynomials on an infinite line. Numerical comparisons are given with a finite difference scheme on a mapped domain as well as a finite element method on a truncated domain.