Can I read A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations on EtoBox?

A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations by Baoli Yin; Jinfeng Wang; Yang Liu; Hong Li is a Engineering article available to read on EtoBox.

What is A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations about?

We aim at analyzing a novel structure preserving difference scheme for the high dimensional nonlinear space-fractional Schrödinger equation. The temporal direction is discretized by the modified Crank-Nicolson scheme, while the spacial variable is approximated by formulas from the shifted convolution quadrature. The energy and mass preserving properties are proved rigorously for the scheme based on the newly developed properties of the coefficients matrix. Further, the optimal convergence rate O ( h 2 + τ 2 ) is derived in detail where h , τ denote the spacial and temporal mesh sizes, respectively. To save the computing cost, we consider the preconditioned fast BiCG (PF-BiCG) algorithm for the resulting complex systems, with the computing complexity of O ( N log ⁡ N ) at each time step and the memory requirement of O ( N ) . Numerical experiments are conducted to confirm our theoretical conclusions and the efficiency of the fast algorithm.

Who reads A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations?

Author

Baoli Yin; Jinfeng Wang; Yang Liu; Hong Li

Publisher

Elsevier BV

Published

2021

Language

EN

Field

Engineering (Physical Sciences)