Efficient numerical methods for initial-value solid-state laser problems

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)