AUTHOREA
Log in
Sign Up
Browse Preprints
LOG IN
SIGN UP
Essential Site Maintenance
: Authorea-powered sites will be updated circa 15:00-17:00 Eastern on Tuesday 5 November.
There should be no interruption to normal services, but please contact us at
[email protected]
in case you face any issues.
Mehran Taghipour
Public Documents
1
An efficient block Gauss-Seidel overrelaxation iteration method for the space fractio...
Hamed Aslani
and 2 more
January 31, 2024
A linearly implicit difference scheme for the space fractional coupled nonlinear Schrödinger (CNLS) equation is proposed. The resulting coefficient matrix of the discretized linear system consists of the sum of a complex scaled identity and a symmetric positive definite, diagonal-plus-Toeplitz, matrix. An efficient block Gauss-Seidel overrelaxation method (BGSOR) method has been established to solve the discretized linear system. It is worth noting that the proposed method solves the linear equations without the need to any system solution, which is beneficial for reducing computational cost and memory requirements. Theoretical analysis implies that the BGSOR method is convergent under a suitable condition. Moreover, an appropriate approach to compute the optimal parameter in the BGSOR method is exploited. Finally, the theoretical analysis is validated by some numerical experiments.