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

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...

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...

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...

RAPPORT Stability of implicit - explicit linear multistep methods

Optimal Explicit Strong-Stability-Preserving General Linear Methods

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A glo...