Details

Autor(en) / Beteiligte

• Wang, Jun‐Gang
• Ran, Yu‐Hong
• Wang, Dong‐Ling

Titel

On structure preserving and circulant preconditioners for the space fractional coupled nonlinear Schrödinger equations

Ist Teil von

• Numerical linear algebra with applications, 2018-08, Vol.25 (4), p.n/a

Ort / Verlag

Oxford: Wiley Subscription Services, Inc

Erscheinungsjahr

2018

Quelle

Access via Wiley Online Library

Beschreibungen/Notizen

• Summary When the implicit, conservative difference scheme with the fractional centered difference formula is employed to discretize the space fractional coupled nonlinear Schrödinger equations, in each time step, we need to solve a complex symmetric linear system. The real part of the coefficient matrix is a symmetric Toeplitz‐plus‐diagonal matrix, whereas the imaginary part is the identity matrix. In this paper, a structure preserving preconditioner and a circulant preconditioner are proposed for such Toeplitz‐like matrix. Theoretically, tight bounds for eigenvalues of the preconditioned matrices are derived. Numerical implementations show that Krylov subspace iteration methods such as BiCGSTAB, when accelerated by the proposed preconditioners, are efficient solvers for solving the discretized linear system.