Related papers: Slow-scale split-step tau-leap method for stiff st…
For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificial-viscosity-based…
We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the…
In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be…
The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant…
Stochastic reaction networks governed by Chemical Langevin Equations (CLE) exhibit pronounced multiscale dynamics spanning fast molecular reactions, intermediate transport, and slow cellular regulation, posing significant challenges for…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
Tau leap schemes were originally designed for the efficient time stepping of discrete state and continuous in time Markov processes arising in stochastic chemical kinetics. Previous convergence results on tau leaping schemes have been…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address…
We analyze and compare the computational complexity of different simulation strategies for Monte Carlo in the setting of classically scaled population processes. This allows a range of widely used competing strategies to be judged…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
A new algorithm, "HiER-leap", is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or…
We discuss systematic extensions of the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order $\tau^2$ for a timestep of length $\tau$, to higher orders in…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with $\tau$-leaping. The task…
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…