Efficiency of exponential time differencing schemes for nonlinear Schrödinger equations
Autor: | Alvaro L. Islas, K. Reger, M. Hederi, C. M. Schober |
---|---|
Rok vydání: | 2016 |
Předmět: |
Numerical Analysis
General Computer Science Breather Applied Mathematics Mathematical analysis Upwind differencing scheme for convection 010103 numerical & computational mathematics Central differencing scheme 01 natural sciences Stiff equation 010305 fluids & plasmas Theoretical Computer Science Exponential function Split-step method Nonlinear system Modeling and Simulation 0103 physical sciences Soliton 0101 mathematics Mathematics |
Zdroj: | Mathematics and Computers in Simulation. 127:101-113 |
ISSN: | 0378-4754 |
DOI: | 10.1016/j.matcom.2013.05.013 |
Popis: | The nonlinear Schrodinger (NLS) equation and its higher order extension (HONLS equation) are used extensively in modeling various phenomena in nonlinear optics and wave mechanics. Fast and accurate nonlinear numerical techniques are needed for further analysis of these models. In this paper, we compare the efficiency of existing Fourier split-step versus exponential time differencing methods in solving the NLS and HONLS equations. Soliton, Stokes wave, large amplitude multiple mode breather, and N-phase solution initial data are considered. To determine the computational efficiency we determine the minimum CPU time required for a given scheme to achieve a specified accuracy in the solution u(x, t) (when an analytical solution is available for comparison) or in one of the associated invariants of the system. Numerical simulations of both the NLS and HONLS equations show that for the initial data considered, the exponential time differencing scheme is computationally more efficient than the Fourier split-step method. Depending on the error measure used, the exponential scheme can be an order of magnitude more efficient than the split-step method. |
Databáze: | OpenAIRE |
Externí odkaz: |