Related papers: Comparing Numerical Integration Schemes for Time-C…
A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit…
Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…
In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we…
This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step and thus the…
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of…
Numerical evolution of time-dependent differential equations via explicit Runge-Kutta or Taylor methods typically fails to preserve symmetries of a system. It is known that there exists no numerical integration method that in general…
The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener…
The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the…
Mixed-precision algorithms combine low- and high-precision computations in order to benefit from the performance gains of reduced-precision without sacrificing accuracy. In this work, we design mixed-precision Runge-Kutta-Chebyshev (RKC)…
This letter summarizes some known properties and also presents several new properties of the Numerical Integration (NI) method for time-optimal trajectory planning along a specified path. The contribution is that rigorous mathematical…
We present high-order, fully explicit projective integration schemes for nonlinear collisional kinetic equations such as the BGK and Boltzmann equation. The methods first take a few small (inner) steps with a simple, explicit method (such…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
Neural networks are a popular tool for modeling sequential data but they generally do not treat time as a continuous variable. Neural ODEs represent an important exception: they parameterize the time derivative of a hidden state with a…
Autonomous vehicles are more likely to be accepted if they drive accurately, comfortably, but also similar to how human drivers would. This is especially true when autonomous and human-driven vehicles need to share the same road. The main…
Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement,…
In this paper, the fourth-order explicit Runge-Kutta method (RK4) is used to make a Deferred Correction (DC) on the explicit midpoint rule, resulting in an explicit one-step method of order six of accuracy, denoted DC6RK2/4. Convergence and…
We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge--Kutta--Legendre (RKL) and Runge--Kutta--Gegenbauer (RKG) super-time-stepping methods were…
We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…