Numerical techniques for the simulation of an ODE-PDE model for supply chains are presented. First, we describe a scheme based on upwind and explicit Euler methods, then provide corrections to maintain positivity of solutions, and finally, prove convergence and provide a convergence rate. The latter is achieved via comparison with wave front tracking solutions and the use of generalized tangent vectors. Different choices of time and space meshes give similar results, both for CPU times and numerical errors. Fast algorithms, based on an accurate choice of time and space meshes and data structures, are then proposed, achieving high computational gains.
An Upwind-Euler scheme for an ODE-PDE model of supply chains
CUTOLO, ALFREDO;PICCOLI, Benedetto
;RARITA', LUIGI
2011
Abstract
Numerical techniques for the simulation of an ODE-PDE model for supply chains are presented. First, we describe a scheme based on upwind and explicit Euler methods, then provide corrections to maintain positivity of solutions, and finally, prove convergence and provide a convergence rate. The latter is achieved via comparison with wave front tracking solutions and the use of generalized tangent vectors. Different choices of time and space meshes give similar results, both for CPU times and numerical errors. Fast algorithms, based on an accurate choice of time and space meshes and data structures, are then proposed, achieving high computational gains.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
