Related papers: Explicit and implicit error inhibiting schemes wit…
In this work, an approximate family of implicit multiderivative Runge-Kutta (MDRK) time integrators for stiff initial value problems is presented. The approximation procedure is based on the recent Approximate Implicit Taylor method (Baeza…
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At…
Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle stiff physical terms implicitly is proposed. Both physical and numerical…
Splitting-based time integration approaches such as fractional steps, alternating direction implicit, operator splitting, and locally one-dimensional methods partition the system of interest into components and solve individual components…
An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order ($p$-order polynomial) modal discontinuous Galerkin method. The core algorithm that based on a global…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
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…
Two-step predictor/corrector methods are provided to solve three classes of problems that present themselves as systems of ordinary differential equations (ODEs). In the first class, velocities are given from which displacements are to be…
This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1…
A semi-implicit-explicit (semi-IMEX) Runge-Kutta (RK) method is proposed for the numerical integration of ordinary differential equations (ODEs) of the form $\mathbf{u}' = \mathbf{f}(t,\mathbf{u}) + G(t,\mathbf{u}) \mathbf{u}$, where…
We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs, admitting a certain error decomposition. This class includes randomized explicit and…
The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible…
This paper continues to study the explicit two-stage fourth-order accurate time discretiza- tions [5, 7]. By introducing variable weights, we propose a class of more general explicit one-step two-stage time discretizations, which are…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
This paper presents a sequence of deferred correction (DC) schemes built recursively from the implicit midpoint scheme for the numerical solution of general first order ordinary differential equations (ODEs). It is proven that each scheme…
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…
Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX…