Extrapolation-based implicit-explicit general linear methods

Extrapolation-based implicit-explicit Peer methods with optimised stability regions

In this paper we investigate an new class of implicit-explicit two-step methods of Peer type for systems of ordinary differential equations with both nonstiff and stiff parts included in the source term. An extrapolation approach based on already computed stage values with equally high consistency order is applied to construct such methods with strong stability properties. Optimised implicit-ex...

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...

High Order Implicit-Explicit General Linear Methods with Optimized Stability Regions

In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For multiphysics problems with both stiff and non-stiff terms implicit-explicit (IMEX) time stepping methods attempt to combine the lower cost advantage of expli...

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...

RAPPORT Stability of implicit - explicit linear multistep methods