Hermite-Galerkin spectral method for Schrödinger-type equation on unbounded domains: Conservation of invariants

发布时间：2026-06-05 作者：浏览次数：

Speaker:	郭士民	DateTime:	2026年6月12日（周五）上午10:00-11:00
Brief Introduction to Speaker: 郭士民，西安交通大学		Place:	国交2号楼315会议室
Abstract:In this talk, we present the finite difference/Hermite-Galerkin spectral methods for Schrödinger-type equations on d-dimensional infinite domains, designed to preserve their invariants. Two classes of problems are considered: the Schrödinger equation with wave operator, and the space-fractional Klein–Gordon–Schrödinger system. The Hermite–Galerkin spectral method is employed for spatial approximation, while the Crank–Nicolson scheme is used for time discretization. The fully discrete numerical schemes are developed, and the conservation properties are established.