Related papers: Signal-Flow Based Runge-Kutta Methods for the Simu…
Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical…
Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a…
Numerous applications necessitate the computation of numerical solutions to differential equations across a wide range of initial conditions and system parameters, which feeds the demand for efficient yet accurate numerical integration…
Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for…
In Spivak's work, dynamical systems are described in terms of their inputs and outputs in a pictorial way using an operad of wiring diagrams. Each dynamical system is a box with certain inputs and outputs, and multiple dynamical systems are…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
This paper proposes a system identification algorithm for systems with multi-rate sensors in a discrete-time framework. It is challenging to obtain an accurate mathematical model when the ratios of inputs and outputs are different in the…
We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong…
A standard approach to solve ordinary differential equations, when they describe dynamical systems, is to adopt a Runge-Kutta or related scheme. Such schemes, however, are not applicable to the large class of equations which do not…
Some properties of numerical time integration methods using summation by parts operators and simultaneous approximation terms are studied. These schemes can be interpreted as implicit Runge-Kutta methods with desirable stability properties…
Strong stability preserving (SSP) Runge-Kutta methods are often desired when evolving in time problems that have two components that have very different time scales. Where the SSP property is needed, it has been shown that implicit and…
Many control, optimization, and learning algorithms rely on discretizations of continuous-time contracting systems, where preservation of contractivity under numerical integration is key for stability, robustness, and reliable fixed-point…
This paper is devoted to examining the stability of Runge-Kutta methods for solving nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous…
Runge-Kutta methods are a popular class of numerical methods for solving ordinary differential equations. Every Runge-Kutta method is characterized by two basic parameters: its order, which measures the accuracy of the solution it produces,…
We investigate a multirate time step approach applied to decoupled methods in fluid and structure interaction(FSI) computation, where two different time steps are used for fluid and structure respectively. For illustration, the multirate…
A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters…
Time-fluctuating signals are ubiquitous and diverse in many physical, chemical, and biological systems, among which random telegraph signals (RTSs) refer to a series of instantaneous switching events between two discrete levels from…
In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes applied to hyperbolic systems with stiff relaxation. In particular, we focus on some recent results on the uniform accuracy for hyperbolic systems with stiff…