Mapped Chebyshev pseudospectral method to study multiple scale phenomena

Details Mapped Chebyshev pseudospectral method to study multiple scale phenomena Mapped Chebyshev pseudospectral method to study multiple scale phenomena

2007-06-21

arxiv.org/abs/0706.3108v2

Physics

Computational Physics

siamltex documentclass; submitted for publication

Scientific paper

In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the spectral interpolation error, the new polynomial-type mapping is compared against previously proposed mappings for the study of collapse and shock wave phenomena. As a physical application, we study the dynamics of two coupled beams, described by coupled nonlinear Schr\"odinger equations and modeling beam propagation in an atomic coherent media, whose spatial sizes differs up to several orders of magnitude. It is demonstrated, also by numerical simulations, that the accuracy properties of the new polynomial-type mapping outperforms in orders of magnitude the ones of the other studied mapping functions.

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