Construction of highly stable implicit-explicit general linear methods

This paper deals with the numerical solution of systems of differential equations with a stiff part and a non-stiff one, typically arising from the semi-discretization of certain partial differential equations models. It is illustrated the construction and analysis of highly stable and high-stage order implicit-explicit (IMEX) methods based on diagonally implicit multistage integration methods (DIMSIMs), a subclass of general linear methods (GLMs). Some examples of methods with optimal stability properties are given. Finally numerical experiments confirm the theoretical expectations.