A unified framework of high order structure-preserving B-splines Galerkin methods for coupled nonlinear Schrödinger systems. (15th November 2021)

• Record Type: Journal Article
• Authors: Castillo, Paul; Gómez, Sergio
• Is Part Of: Computers & mathematics with applications. Volume 102(2021)
• Page Start: 45
• Page End: 53
• Publication Date: 2021-11-15
• Subjects: Coupled nonlinear Schrödinger equations -- B-splines finite element method -- Mass and energy conservation -- Composition methods; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.10.007
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Using a general computational framework, we derive an optimal error estimate in the L 2 norm for a semi discrete method based on high order B-splines Galerkin spatial discretizations, applied to a coupled nonlinear Schrödinger system with cubic nonlinearity. A fully discrete method based on a conservative nonlinear splitting Crank-Nicolson time step is then proposed; and conservation of the mass and the energy is theoretically proven. To validate its accuracy in space and time, and its conservation properties, several numerical experiments are carried out with B-splines up to order 7.