Uniform Error Bounds of an Energy-Preserving Exponential Wave Integrator Fourier Pseudo-Spectral Method for the Nonlinear Schrödinger Equation with Wave Operator and Weak Nonlinearity
Jiyong Li
Abstract:Recently, the numerical methods for long-time dynamics of PDEs with weak nonlinearity have received more and more attention. For the nonlinear Schrödinger equation (NLS) with wave operator (NLSW) and weak nonlinearity controlled by a small value ε ∈ (0, 1], an exponential wave integrator Fourier pseudo-spectral (EWIFP) discretization has been developed (Guo et al., 2021) and proved to be uniformly accurate about ε up to the time at O(1/ε 2 ). However, the EWIFP method is not time symmetric and can not preserve… Show more
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