Solving random boundary heat model using the finite difference method under mean square convergence. Issue 3 (17th April 2019)

• Record Type: Journal Article
• Authors: Cortés, J.‐C.; Romero, J.‐V.; Roselló, M.‐D.; Sohaly, M.A.
• Is Part Of: Computational and mathematical methods. Volume 1:Issue 3(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-17
• Subjects: mean square consistency -- mean square stability -- random boundary heat model -- random difference scheme; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1026
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : 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.