An adaptive multilevel approach to parabolic equations I.: general theory and 1D implementation
IMPACT of Computing in Science and Engineering
An adaptive multilevel approach to parabolic equations
IMPACT of Computing in Science and Engineering
The Mathematics of Infectious Diseases
SIAM Review
Wavelet methods for PDEs — some recent developments
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A solver for the stochastic master equation applied to gene regulatory networks
Journal of Computational and Applied Mathematics
Hybrid method for the chemical master equation
Journal of Computational Physics
A Hierarchy of Approximations of the Master Equation Scaled by a Size Parameter
Journal of Scientific Computing
Adaptive solution of the master equation in low dimensions
Applied Numerical Mathematics
Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation
SIAM Journal on Scientific Computing
Fokker–Planck approximation of the master equation in molecular biology
Computing and Visualization in Science
Spectral approximation of solutions to the chemical master equation
Journal of Computational and Applied Mathematics
Solving chemical master equations by adaptive wavelet compression
Journal of Computational Physics
Hybrid numerical solution of the chemical master equation
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
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An adaptive wavelet method for the chemical master equation is constructed. The method is based on the representation of the solution in a sparse Haar wavelet basis, the time integration by Rothe's method, and an iterative procedure which in each time-step selects those degrees of freedom which are essential for propagating the solution. The accuracy and efficiency of the approach is discussed, and the performance of the adaptive wavelet method is demonstrated by numerical examples.