Abstract

SUXO MAMANI, Franz. SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY THE MONTECARLO METHOD. Revista Boliviana de Física [online]. 2011, vol.19, n.19, pp.24-33. ISSN 1562-3823.

We use the Monte Carlo method to obtain solutions of partial differential equations (PDE) such as the Laplace equation for a flat irregular region and the heat equation for a flat circular and regular region. With this method we simulate random walks in the discrete regions that result from the PDE developed as finite differences. The discretization process limits the possible directions between the region nodes and assigns them transition probabilities. To determine the value of the node (i.e., the solution for a point in the discretized region) we launch from the node several particles and let them evolve according to their probabilities until they reach the boundary region, which is the boundary condition for the PDE. We present the results of this method for the heat equation in a thin board for six different instants. For the Laplace equation the results correspond to two different physical systems: a stationary and elastic thin membrane and the stationary temperature distribution of a thin board.

Keywords : computational techniques and simulations; finite-difference methods; applications of Monte Carlo methods.

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