The Class of Implicit-explicit General Linear Methods for Ordinary Differential Equations

The class of implicit-explicit (IMEX) methods are numerical scheme designed for numerical solution of ordinary differential systems with splitting of the right hand sides of the differential systems into two parts, one of which is non-stiff or mildly stiff, and suitable for explicit time integration, and the other part is stiff, and suitable for implicit time integration. We described the construction of IMEX general linear methods with desired stability properties. Under suitable assumptions such as the form of coefficient matrices, order and stage order of methods, the form of stability function we attempt to maximize the combined region of absolute stability. Finally, we apply constructed methods to a series of test problems. References [1] M. Bras, A. Cardone, Z. Jackiewicz, P. Pierzchala, Error propagation for implicit-explicit general linear methods, Appl. Numer. Math., 131 (2018), pp. 207–231. [2] A. Cardone, Z. Jackiewicz, A. Sandu, H. Zhang, Extrapolation-based implicit–explicit general linear methods, Numer. Algorithms, 65 (2014), pp. 377—399