Initial-Boundary Value Problem for the heat equation - A stochastic algorithm
Probability
2016-10-14 v1
Abstract
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirich-let problem for Laplace's equation, its implementation is rather easy. The definition of the random walk is based on a new mean value formula for the heat equation. The convergence results and numerical examples permit to emphasize the efficiency and accuracy of the algorithm.
Cite
@article{arxiv.1610.03963,
title = {Initial-Boundary Value Problem for the heat equation - A stochastic algorithm},
author = {Madalina Deaconu and Samuel Herrmann},
journal= {arXiv preprint arXiv:1610.03963},
year = {2016}
}