In this paper, we consider an approach to improve the performance of exponential Runge–
Kutta integrators and Lawson schemes in cases where the solution of a related, but usually …

In this work, we design and investigate contrast-independent partially explicit time
discretizations for wave equations in heterogeneous high-contrast media. We consider …

This work continues a line of work on developing partially explicit methods for multiscale
problems. In our previous works, we considered linear multiscale problems where the …

Traditional step-size controllers make the tacit assumption that the cost of a time step is
independent of the step size. This is true for explicit and implicit integrators that use direct …

The automatic selection of an appropriate time step size has been considered extensively in
the literature. However, most of the strategies developed operate under the assumption that …

Nonlinear time fractional partial differential equations are widely used in modeling and
simulations. In many applications, there are high contrast changes in media properties. For …

Abstract Systems driven by multiple physical processes are central to many areas of science
and engineering. Time discretization of multiphysics systems is challenging, since different …

In the paper, we study a design and stability of contrast-independent partially explicit time
discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media …

In this paper we consider an approach to improve the performance of exponential Runge--
Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually …

Time integration methods for solving initial value problems are an important component of
many scientific and engineering simulations. Implicit time integrators are desirable for their …