Abstract
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.
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The authors thank Springer Nature Submission Support’s suggestion.
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This work is supported by the National Natural Science Foundation of China (Granted No. 11961008(X. Luo), 71961003(S.W. Xiang)).
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X. Luo and C. Ye proposed the idea; T. Yao and X. Luo given the analysis; C. Ye prepared numerical test and figures. T. Yao and X. Luo wrote the main manuscript text. All authors reviewed the manuscript.
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Yao, T., Ye, C., Luo, X. et al. An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs. Numer Algor 94, 643–668 (2023). https://doi.org/10.1007/s11075-023-01514-z
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DOI: https://doi.org/10.1007/s11075-023-01514-z