Optimal error estimate of a conformal Fourier pseudo‐spectral method for the damped nonlinear Schrödinger equation
Copyright policy )Optimal error estimate of a conformal Fourier pseudo‐spectral method for the damped nonlinear Schrödinger equation
In this article, a Fourier pseudospectral method, which preserves the conforal conservation la, is proposed for solving the damped nonlinear Schrödinger equation. Based on the energy method and the semi‐norm equivalence between the Fourier pseudospectral method and the finite difference method, a priori estimate for the new method is established, which shows that the proposed method is unconditionally convergent with order ofin the discrete‐norm, whereis the time step andis the number of collocation points used in the spectral method. Some numerical results are addressed to confirm our theoretical analysis.
- Nanjing Normal University China (People's Republic of)
Error bounds for initial value and initial-boundary value problems involving PDEs, Fixed-point theorems, damped nonlinear Schrödinger equation, NLS equations (nonlinear Schrödinger equations), priori estimate, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fourier pseudo-spectral method, Numerical methods for discrete and fast Fourier transforms, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Error bounds for initial value and initial-boundary value problems involving PDEs, Fixed-point theorems, damped nonlinear Schrödinger equation, NLS equations (nonlinear Schrödinger equations), priori estimate, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fourier pseudo-spectral method, Numerical methods for discrete and fast Fourier transforms, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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