Abstract
Mean value theorems often use to construct statistical unbiased estimators for the solutions of boundary value problems for PDEs. Every such theorem determines integral equation for PDE’s solution in the space of bounded function in some compact set. The norm of integral operator is one in case of first boundary condition. We formulate the conditions suffice to apply von-Neumann–Ulam scheme for this equation. It is shown that conditions are fulfilled for well-known statistical algorithms for PDEs.
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Work is supported by RFBR grant 14-01-00271a.
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Sipin, A. (2014). Monte Carlo Method for Partial Differential Equations. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_46
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DOI: https://doi.org/10.1007/978-1-4939-2104-1_46
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