Preconditioned iterative solver for 2D complex fractional Ginzburg-Landau equation

In the work, we exploit the preconditioned conjugate orthogonal conjugate gradient (PCOCG) algorithm to solve the complex symmetric linear systems of equations arising from 2D spatial complex fractional Ginzburg-Landau equation (GLE). The matrix in the linear systems of equations is equal to a symmetric block Toeplitz matrix plus a complex diagonal matrix. Moreover, the effective
$\tau$
preconditioner is proposed to accelerate the rate of convergence of the iterative algorithm. Two numerical experiments are carried out to indicate the computational merit of the proposed method.