An Upwind-Euler Scheme for an ODE-PDE Model of Supply Chains

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, provide corrections to maintain positivity of solutions, prove convergence and provide convergence rate. The latter is achieved via comparison with Wave Front Tracking solutions and the use of generalized tangent vectors. Different choice 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.