Optimal Error Bounds for Exponential Wave Integrators for Fractional Schrodinger Equations
Rigorous convergence analysis of an exponential wave integrator (EWI) Fourier spectral scheme for the space-fractional nonlinear Schrodinger equation when the potential and nonlinearity have only low regularity. Under an L-infinity potential, a C1 nonlinearity and an H-alpha solution, it proves an optimal first-order L2 error bound in time and an optimal spatial bound with no CFL-type step-size restriction, plus sharper bounds in the energy norm. Shows how to obtain optimal, restriction-free error estimates for a fractional dispersive PDE at minimal smoothness.
Optimal error bounds on an exponential wave integrator Fourier spectral method for fractional
This paper establishes optimal error bounds for an exponential wave integrator (EWI) applied to the space-fractional nonlinear Schrodinger equation when the potential and nonlinearity have low regula…