Stability properties of implicit-explicit multistep methods for a class of nonlinear parabolic equations (Q2814438)

This paper is concerned with stability of the implicit-explicit multistep methods for a class of nonlinear parabolic equations of type \(u'(t)+A(t)u(t)=B(t,u(t))\), \(u(0)=u^0\), posed in a general Hilbert space \(H\). The setting of such parabolic equations considered by the author includes the case of complex Ginzburg-Landau equation or the generalized cubic-quintic complex Swift-Hohenberg equation. The stability of the scheme is obtained by combining an implicit scheme for the discretization of the linear part and an explicit scheme for the discretization of the nonlinear part of the equation under a best possible linear stability condition.