 Revisiting Kac’s method: A Monte Carlo algorithm for solving the Telegrapher’s equationsBolong Zhang, Wenjian Yu and Michael Mascagni Mathematics and Computers in Simulation (MATCOM), 2019, vol. 156, issue C, 178-193 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. Keywords: Hyperbolic partial differential equation; Kac’s stochastic model; Monte Carlo method; Numerical algorithm; The telegrapher’s equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:156:y:2019:i:c:p:178-193 DOI: 10.1016/j.matcom.2018.08.007 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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