Open AccessSolving random boundary heat model using the finite difference method under mean square convergence
Author(s) -
Cortés J.C.,
Romero J.V.,
Roselló M.D.,
Sohaly M.A.
Publication year - 2019
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1026
Subject(s) - convergence (economics) , square (algebra) , mean square , boundary (topology) , mathematics , mean difference , boundary value problem , statistics , mathematical analysis , geometry , confidence interval , economics , economic growth
This contribution is devoted to construct numerical approximations to the solution of the one‐dimensional boundary value problem for the heat model with uncertainty in the diffusion coefficient. Approximations are constructed via random numerical schemes. This approach permits discussing the effect of the random diffusion coefficient, which is assumed a random variable. We establish results about the consistency and stability of the random difference scheme using mean square convergence. Finally, an illustrative example is presented.