We deal with the numerical scheme for the Liouville Master Equation (LME) of a kind of Piecewise Deterministic Processes (PDP) with memory, analysed in [2]. The LME is a linear system of hyperbolic PDEs, written in non?conservative form, with non-local boundary conditions. The solutions of that equation are time dependent marginal distribution functions whose sum satisfies the total probability conservation law. In [2] the convergence of the numerical scheme, based on the Courant-Isaacson-Rees jointly with a direct quadrature, has been proved under a Courant-Friedrichs-Lewy like (CFL) condition. Here we show that the numerical solution is monotonic under a similar CFL condition. Moreover, we evaluate the conservativity of the total probability for the calculated solution. Finally, an implementation of a parallel algorithm by using the MPI library is described and the results of some performance tests are presented.

A finite difference method for piecewise deterministic processes with memory II

ANNUNZIATO, Mario
2009-01-01

Abstract

We deal with the numerical scheme for the Liouville Master Equation (LME) of a kind of Piecewise Deterministic Processes (PDP) with memory, analysed in [2]. The LME is a linear system of hyperbolic PDEs, written in non?conservative form, with non-local boundary conditions. The solutions of that equation are time dependent marginal distribution functions whose sum satisfies the total probability conservation law. In [2] the convergence of the numerical scheme, based on the Courant-Isaacson-Rees jointly with a direct quadrature, has been proved under a Courant-Friedrichs-Lewy like (CFL) condition. Here we show that the numerical solution is monotonic under a similar CFL condition. Moreover, we evaluate the conservativity of the total probability for the calculated solution. Finally, an implementation of a parallel algorithm by using the MPI library is described and the results of some performance tests are presented.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1993099
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