Revisiting Kac’s method: A Monte Carlo algorithm for solving the Telegrapher’s equations

Abstract

In this work, we use Kac’s stochastic model to derive a Monte Carlo (MC) algorithm for the numerical solution of the telegrapher’s equation. The major ideas are to use random values under exponential distribution to facilitate the calculation of the random time, and to accelerate the simulation for multiple points through recycling random time simulation. Compared with the MC method recently proposed by Acebrón and Ribeiro, the Kac’s model based method is able to handle two-dimensional (2-D) and higher-dimensional problems with unbounded domain, and 2-D bounded-domain problems with the homogeneous boundary condition. Moreover, it has an efficient algorithmic implementation. With numerical experiments, we have validated the accuracy and efficiency of the proposed algorithms, and their applicability to some 2-D telegrapher’s equations.