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Solving chemical master equations by adaptive wavelet compression. (English) Zbl 1203.65104
After the introduction of the chemical master equation (CME) the approximation of the solution of the CME by means of wavelets is discussed. The solution is represented in a sparse wavelet basis which is adapted in each time step. At first, a wavelet method which is only adaptive in space is considered. Hereby, a 2-stage Gauss-Runge-Kutta method and higher order Daubechies wavelets are used. Then, a strategy for choosing the step-size in time adaptively is proposed. Four numerical examples are presented to demonstrate the performance of the adaptive wavelet method.

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