Two new implicit–explicit, additive Runge–Kutta (ARK 2) methods are given with fourth-and
fifth-order formal accuracies, respectively. Both combine explicit Runge–Kutta (ERK) …

We investigate implicit–explicit (IMEX) Runge–Kutta (RK) methods for differential systems
with non-stiff and stiff processes. The construction of such methods with large regions of …

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 …

Excerpt This book focuses on IMEX methods, with particular emphasis on their application to
systems of PDEs. IMEX methods have proven to be highly effective for solving a wide range …

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 of …

We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–
Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The …

This work focuses on the development of a new class of high-order accurate methods for
multirate time integration of systems of ordinary differential equations. Unlike other recent …

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 …

In this work we construct a multiderivative implicit-explicit (IMEX) scheme for a class of stiff
ordinary differential equations (ODEs). Our solver is high-order accurate and has an …

This paper compares and contrasts higher-order, semi-implicit temporal integration
strategies for the incompressible Navier–Stokes methods based on spectral deferred …