Solving chemical master equations by adaptive wavelet compression

DOI10.1016/j.jcp.2010.04.015zbMath1203.65104OpenAlexW2011894114MaRDI QIDQ983027

Tobias Jahnke, Tudor Udrescu

Publication date: 28 July 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://publikationen.bibliothek.kit.edu/1000018826/1375655

zbMATH Keywords

numerical examplesgene regulatory networksRothe's methodstep-size controlchemical master equationstochastic reaction kineticswavelet compressionadaptive Galerkin approximationadaptive step-size selectionGauss-Runge-Kutta method

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Neural networks for/in biological studies, artificial life and related topics (92B20) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for wavelets (65T60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (9)

Extending the multi-level method for the simulation of stochastic biological systems ⋮ Conditional Monte Carlo for Reaction Networks ⋮ Stochastic modeling and numerical simulation of gene regulatory networks with protein bursting ⋮ Local error estimates for adaptive simulation of the reaction-diffusion master equation via operator splitting ⋮ Block-tridiagonal state-space realization of chemical master equations: a tool to compute explicit solutions ⋮ The Exit Time Finite State Projection Scheme: Bounding Exit Distributions and Occupation Measures of Continuous-Time Markov Chains ⋮ Hybrid discrete/continuum algorithms for stochastic reaction networks ⋮ Markovian dynamics on complex reaction networks ⋮ Finite state projection for approximating the stationary solution to the chemical master equation using reaction rate equations

Uses Software

• RODAS

Cites Work

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• A dynamical low-rank approach to the chemical master equation
• Solving the chemical master equation for monomolecular reaction systems analytically
• A solver for the stochastic master equation applied to gene regulatory networks
• Sparse grids and hybrid methods for the chemical master equation
• Adaptive solution of the master equation in low dimensions
• Spectral approximation of solutions to the chemical master equation
• Adaptive wavelet methods. II: Beyond the elliptic case
• Hybrid method for the chemical master equation
• A hierarchy of approximations of the master equation scaled by a size parameter
• The Mathematics of Infectious Diseases
• Space-time adaptive wavelet methods for parabolic evolution problems
• An Adaptive Wavelet Method for the Chemical Master Equation
• Multiscale Modeling of Chemical Kinetics via the Master Equation
• Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation
• Ten Lectures on Wavelets
• Adaptive wavelet methods for elliptic operator equations: Convergence rates
• Numerical solution of parabolic equations in high dimensions
• Wavelet methods for PDEs -- some recent developments
• Fokker–Planck approximation of the master equation in molecular biology

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