In this paper we investigate the behaviour of the numerical solution of the Liouville---Master Equation (LME) for time dependent distributions, that arises by the statistical characterisation of a class of piecewise deterministic stochastic processes (PDP). This is a system of linear hyperbolic PDEs with non-constant coefficients. The numerical solution is found by means of upwind and forward Euler scheme. We find a Courant---Friedrichs---Lewy condition ensuring both convergence and monotonicity of the numerical solution. In particular, the global error is shown to be bounded by a linear increasing in the integration time, under an appropriate norm. Some numerical tests for known analytical solutions of practical problems verify the theoretical findings.
Analysis of upwind method for piecewise deterministic Markov processes
ANNUNZIATO, Mario
2008-01-01
Abstract
In this paper we investigate the behaviour of the numerical solution of the Liouville---Master Equation (LME) for time dependent distributions, that arises by the statistical characterisation of a class of piecewise deterministic stochastic processes (PDP). This is a system of linear hyperbolic PDEs with non-constant coefficients. The numerical solution is found by means of upwind and forward Euler scheme. We find a Courant---Friedrichs---Lewy condition ensuring both convergence and monotonicity of the numerical solution. In particular, the global error is shown to be bounded by a linear increasing in the integration time, under an appropriate norm. Some numerical tests for known analytical solutions of practical problems verify the theoretical findings.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
