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Implicit ODE solvers with good local error control for the transient analysis of Markov models. (English) Zbl 1411.65092
Summary: Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMCs, many implicit ODE solvers are such that the linear systems involved in their steps can be solved by using iterative methods with strict control of the 1-norm of the error. This allows the development of implementations of those ODE solvers for the transient analysis of CTMCs that can be more efficient and more accurate than more standard implementations.
MSC:
65L05 Numerical methods for initial value problems
60J27 Continuous-time Markov processes on discrete state spaces
65C40 Numerical analysis or methods applied to Markov chains
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