Adaptive time-stepping for the strong numerical solution of stochastic differential equations

2014 ◽  
Vol 68 (4) ◽  
pp. 791-812 ◽  
Author(s):  
Silvana Ilie ◽  
Kenneth R. Jackson ◽  
Wayne H. Enright
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Stochastic Differential Equations ◽  
Time Stepping ◽  
Adaptive Time ◽  
Adaptive Time Stepping

scholarly journals Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation

2021 ◽  
Author(s):  
Jill Marie Anderson Padgett
Keyword(s):  
Numerical Solution ◽  
Master Equation ◽  
Reaction Diffusion ◽  
Stochastic Simulation Algorithm ◽  
Cellular Processes ◽  
Time Stepping ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
And Diffusion ◽  
Adaptive Time Stepping

Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.

scholarly journals Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation

2021 ◽  
Author(s):  
Jill Marie Anderson Padgett
Keyword(s):  
Numerical Solution ◽  
Master Equation ◽  
Reaction Diffusion ◽  
Stochastic Simulation Algorithm ◽  
Cellular Processes ◽  
Time Stepping ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
And Diffusion ◽  
Adaptive Time Stepping

Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

scholarly journals Digital filters in adaptive time-stepping

2003 ◽  
Vol 29 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Gustaf Söderlind
Keyword(s):  
Digital Filters ◽  
Time Stepping ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Numerical solution of stochastic differential equations

1994 ◽  
Vol 47 (1-2) ◽  
pp. 121-126 ◽  
Author(s):  
Denis Talay
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Stochastic Differential Equations

scholarly journals An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

2021 ◽  
Vol 379 ◽  
pp. 203-216
Author(s):  
Hariswaran Sitaraman ◽  
Deepthi Vaidhynathan ◽  
Ray Grout ◽  
Thomas Hauser ◽  
Christine M. Hrenya ◽  
...  
Keyword(s):  
Time Stepping ◽  
Dem Simulations ◽  
Adaptive Time ◽  
Adaptive Time Stepping

scholarly journals The composite Milstein methods for the numerical solution of Ito stochastic differential equations

2011 ◽  
Vol 235 (8) ◽  
pp. 2277-2299 ◽  
Author(s):  
M.A. Omar ◽  
A. Aboul-Hassan ◽  
S.I. Rabia
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Stochastic Differential Equations
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