Ten lectures on wavelets
The Mathematics of Infectious Diseases
SIAM Review
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
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
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Spectral approximation of solutions to the chemical master equation
Journal of Computational and Applied Mathematics
An Adaptive Wavelet Method for the Chemical Master Equation
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
Solving chemical master equations numerically on a large state space is known to be a difficult problem because the huge number of unknowns is far beyond the capacity of traditional methods. We present an adaptive method which compresses the problem very efficiently by representing the solution in a sparse wavelet basis that is updated in each step. The step-size is chosen adaptively according to estimates of the temporal and spatial approximation errors. Numerical examples demonstrate the reliability of the error estimation and show that the method can solve large problems with bimodal solution profiles.