Local error estimation for implicit-explicit general linear methods

Implicit-explicit general linear methods are investigated, for the numerical solution of differential systems with mildly stiff and non-stiff parts. Stage order and order conditions are formulated. Local error estimations are derived, both for uniform and nonuniform meshes. Suitable rescaling techniques for variable step algorithms are discussed. The construction of such methods, characterized by high stage order and favorable stability properties, is also presented. Numerical experiments support the theoretical expectations regarding both the accuracy of the schemes and the estimation of the local error.