Parallel Implicit-Explicit General Linear Methods

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

Explicit Parallel Resolvent Methods for System of General Variational Inclusions

In this paper, we introduce and consider a new system of extended general variational inclusions involving eight different operators. Using the resolvent operator techniques, we show that the new system of extended general variational inclusions is equivalent to the fixed point problem. We prove the strong convergence of some new explicit iterative parallel algorithms using resolvent methods un...