Abstract
AbstractIn this paper, we take the space fractional nonlinear Schrödinger as an example to establish the L∞ convergence error analysis for the conservative Fourier pseudo‐spectral method, which has not been studied. We introduce a new fractional Sobolev norm to construct the discrete fractional Sobolev space, and also prove some important lemmas for the new fractional Sobolev norm. Based on these lemmas and energy method, a priori error estimate for the method can be established. Then, we are able to prove that the Fourier pseudo‐spectral method is unconditionally convergent with order O(τ2 + Nα/2 − r) in the discrete L∞ norm, where τ is the time step and N is the number of collocation points used in the spectral method. Numerical examples are presented to verify the theoretical analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Numerical Methods for Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
