General linear methods

High order implicit-explicit general linear methods with optimized stability regions

textcopyright 2016 Society for Industrial and Applied Mathematics. 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 …

Application of implicit-explicit general linear methods to reaction-diffusion problems

textcopyright 2015 AIP Publishing LLC. Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equations with both stiff and nonstiff components. We have recently proposed new implicit-explicit methods of general linear type …

Extrapolation-based implicit-explicit general linear methods

For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit …

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 …

A second-order diagonally-implicit-explicit multi-stage integration method

Implicit-explicit time stepping methods have proved useful for efficiently solving problems with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX multistep methods have been studied in the literature. But there are no available …