An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs

[摘要] An ensemble-based time stepping scheme is applied to solving a transient heat equation with random Robin boundary and diffusion coefficients. By introducing two ensemble means of Robin boundary and diffusion coefficients, we propose a new ensemble Monte Carlo (EMC) scheme for the transient heat equation. The EMC scheme solves a single linear system including several right-side vectors at each time step. Stability analysis and error estimates are derived. Two numerical examples verify the theoretical results and the validity of the EMC method.

[效力级别]  Early Access

[关键词] PARTIAL-DIFFERENTIAL-EQUATIONS;STOCHASTIC COLLOCATION METHOD;ROBIN COEFFICIENT;ALGORITHM