On Extension the Stability Region of Implicit-Explicit Linear Multistep Methods for Ordinary Differential Equation

Stability of implicit - explicit linear multistep methods

In many applications, large systems of ordinary di erential equations (ODEs) have to be solved numerically that have both sti and nonsti parts. A popular approach in such cases is to integrate the sti parts implicitly and the nonsti parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linea...

RAPPORT Stability of implicit - explicit linear multistep methods

Variable Step-size Implicit-explicit Linear Multistep Methods for Time-dependent Partial Differential Equations

Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily impleme...

Partitioned and Implicit-Explicit General Linear Methods for Ordinary Differential Equations

Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equations with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this paper we study new implicit-explicit methods of general linear type (IMEX-GLMs). We develop an order conditions theory for high stage order partitioned GLMs tha...

Stability of Implicit and Implicit–explicit Multistep Methods for Nonlinear Parabolic Equations

We analyze the discretization of nonlinear parabolic equations in Hilbert spaces by both implicit and implicit–explicit multistep methods and establish local stability under best possible and best possible linear stability conditions, respectively. Our approach is based on suitable quantifications of the non-self-adjointness of linear elliptic operators and a discrete perturbation argument.