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Stochastic and Perturbation Methods in PDE Systems


The Stochastic and Perturbation Methods in Partial Differential Equation (PDE) Systems program developed new mathematical capabilities for next-generation DoD challenges in applications where PDE models are used to represent physical systems. Particular mathematical challenges addressed were parameter uncertainty, accurate interpolation and extrapolation using known solutions, and treatment of problems involving wide disparity of spatial scales. This program was structured around three key objectives:

1.  Advancing stochastic methodology for PDE systems.
2.  Developing interpolation and extrapolation techniques in parameter
3.  Establishing new approaches for hybridization across spatial scale.





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