Adaptive solution of the master equation in low dimensions

The master equation satisfied by a probability density function is solved on a grid with a cell size h>1. A modified master equation is derived for the time development of the average of the density in the larger cells. The accuracy of the approximation is studied and the total probability is conserved. Based on an estimate of the discretization error, the cell size is dynamically adapted to the solution. The method is suitable for a few space dimensions and is tested on a model for the migration of people. Substantial savings in memory requirements and CPU times are reported in numerical experiments.