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Efficient numerical methods for initial‐value solid‐state laser problems
Author(s) -
Feng Fan,
Pflaum Christoph
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210316
Subject(s) - zero (linguistics) , state (computer science) , oscillation (cell signaling) , initial value problem , exact solutions in general relativity , stability (learning theory) , numerical analysis , mathematics , laser , stiffness , computer science , algorithm , mathematical optimization , control theory (sociology) , mathematical analysis , physics , optics , control (management) , artificial intelligence , chemistry , thermodynamics , philosophy , biochemistry , linguistics , machine learning
Abstract The difficulties of solving initial‐value solid‐state laser problems numerically arise from both stiffness of the problems and near‐to‐zero nonnegative exact solutions. Stability and non‐negativity must be maintained simultaneously in the numerical solutions. Backward differentiation formulas (BDFs) is capable of dealing with stiff problems ,but is of small oscillation when time‐step is large. Therefore unfortunately BDFs suffers from severe time‐step restriction . In this paper,we present an optimized numerical approach, with which 3‐dimensional laser problems can be solved faster and much more efficiently. These techniques can not only be used for solid‐state laser systems, but can also be applied to solve other stiff problems which have near‐to‐zero nonnegative exact solutions. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)