Variable stepsize implementation of implicit-explicit general linear methods

For effcient integration of such kind of systems we consider implicit-explicit (IMEX) methods, where the non-stiff part f(y) is integrated by an explicit numerical scheme, and the stiff part g(y) is integrated by an implicit numerical scheme. After the investigation of IMEX Runge-Kutta (RK) methods [1], and IMEX General Linear Methods (GLMs) [2, 3] in a fixed stepsize formulation, we focus on estimation of local discretization errors and rescaling stepsize techniques for high stage order IMEX GLMs in fixed and variable stepsize environments. We also describe the construction of such methods with desirable accuracy and stability properties. References [1] G. Izzo and Z. Jackiewicz, Highly stable implicit-explicit Runge-Kutta methods, Appl. Numer. Math., 113 (2017), 71{92. [2] M. Bras, G. Izzo and Z. Jackiewicz, Accurate Implicit{Explicit General Linear Methods with Inherent Runge{Kutta Stability, J. Sci. Comput., 70 (2017), 1105-1143. [3] G. Izzo and Z. Jackiewicz, Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part, Numer. Algorithms, 2019 (in press).