Parallel split-step Fourier methods for nonlinear Schrödinger-type equations. (English) Zbl 1047.65072

Xu, Xiangming; Taha, Thiab

J. Math. Model. Algorithms 2, No. 3, 185-201 (2003).

Summary: The nonlinear Schrödinger equation is of tremendous interest in both theory and applications. Various regimes of pulse propagation in optical fibers are modeled by some form of the nonlinear Schrödinger equation.
In this paper we introduce sequential and parallel split-step Fourier methods for numerical simulations of the nonlinear Schrödinger-type equations. The parallel methods are implemented on the Origin 2000 multiprocessor computer. Our numerical experiments have shown that these methods give accurate results and considerable speedup.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55	NLS equations (nonlinear Schrödinger equations)
65T50	Numerical methods for discrete and fast Fourier transforms
65Y05	Parallel numerical computation

Keywords:

split-step method; parallel algorithms; nonlinear Schrödinger equation; Fourier methods; numerical experiments