On a one-dimensional Schro¨dinger-Poisson scattering model
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Journal of Computational Physics
Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
SIAM Journal on Scientific Computing
Solution of time-independent Schrödinger equation by the imaginary time propagation method
Journal of Computational Physics
High-order time-splitting Hermite and Fourier spectral methods
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
On the computation of ground state and dynamics of Schrödinger-Poisson-Slater system
Journal of Computational Physics
Hi-index | 31.45 |
Efficient and accurate numerical methods are presented for computing ground states and dynamics of the three-dimensional (3D) nonlinear relativistic Hartree equation both without and with an external potential. This equation was derived recently for describing the mean field dynamics of boson stars. In its numerics, due to the appearance of pseudodifferential operator which is defined in phase space via symbol, spectral method is more suitable for the discretization in space than other numerical methods such as finite difference method, etc. For computing ground states, a backward Euler sine pseudospectral (BESP) method is proposed based on a gradient flow with discrete normalization; and respectively, for computing dynamics, a time-splitting sine pseudospectral (TSSP) method is presented based on a splitting technique to decouple the nonlinearity. Both BESP and TSSP are efficient in computation via discrete sine transform, and are of spectral accuracy in spatial discretization. TSSP is of second-order accuracy in temporal discretization and conserves the normalization in discretized level. In addition, when the external potential and initial data for dynamics are spherically symmetric, the original 3D problem collapses to a quasi-1D problem, for which both BESP and TSSP methods are extended successfully with a proper change of variables. Finally, extensive numerical results are reported to demonstrate the spectral accuracy of the methods and to show very interesting and complicated phenomena in the mean field dynamics of boson stars.