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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
