Related papers: Adaptive time-stepping for aggregation-shattering …
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta methods, the new methods yield expected convergence…
We report a novel approach for the efficient computation of solutions of a broad class of large-scale systems of non-linear ordinary differential equations, describing aggregation kinetics. The method is based on a new take on the…
The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods differ from additive RK methods in that their coefficients are…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the…
We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a dissipation potential, which is positively homogeneous of…
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…
We introduce an explicit, adaptive time-stepping scheme for the simulation of SPDEs with one-sided Lipschitz drift coefficients. Strong convergence rates are proven for the full space-time discretisation with multiplicative trace-class…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have an embedded scheme, i.e., that have local error estimation…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
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 this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to…
Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the model is solved numerically. We propose to ensure positivity or other…
Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a significant challenge due to the difference in physics, temporal, and spatial scales. This study explores…
We show that adaptive time stepping in particle accelerator simulation is an enhancement for certain problems. The new algorithm has been implemented in the OPAL (Object Oriented Parallel Accelerator Library) framework, and is compared to…
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. The proposed methods are based on a specific subset of explicit one-step…
Cell collective migration plays a crucial role in a variety of physiological processes. In this work, we propose the Runge-Kutta random feature method to solve the nonlinear and strongly coupled multiphase flow problems of cells, in which…
Time integration of ODEs or time-dependent PDEs with required resolution of the fastest time scales of the system, can be very costly if the system exhibits multiple time scales of different magnitudes. If the different time scales are…