Read e-book online Asymptotic solutions of differential equations and their PDF

By Calvin H. Wilcox

ISBN-10: 0471943851

ISBN-13: 9780471943853

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Extra info for Asymptotic solutions of differential equations and their applications

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The FAST method) the number of required model evaluations becomes rapidly impractical for realistic, large-scale models involving many parameters. , for large time-dependent systems). Furthermore, since the response sensitivities and parameter uncertainties are inherently amalgamated, improvements in parameter uncertainties cannot be directly propagated to improve response uncertainties; rather, the entire set of simulations must be repeated anew. Currently, a general-purpose “fool-proof” statistical method for analyzing correctly mathematical models of physical processes involving highly correlated parameters does not seem to exist, so that particular care must be used when interpreting regression results for such models.

Although the SFRD is Copyright © 2005 Taylor & Francis Group, LLC 26 Sensitivity and Uncertainty Analysis relatively efficient computationally, it lacks precision and cannot detect parameters whose effects cancel each other out. The IFFD estimates the main and quadratic effects, and two-parameter interactions between the most influential parameters. Although the IFFD requires fewer computations than the total number of model parameters, the IFFD gives good results only if the model’s response is actually influenced by only a few truly important parameters.

Hence, screening design methods should be used cautiously, since they may be a priori inadequate to identify the truly important parameters. On the other hand, “sampling-based uncertainty and sensitivity analysis” is performed in order to ascertain if model predictions fall within some region of concern (“uncertainty in model responses due to uncertainties in model parameters”) and to identify the dominant parameters in contributing to the response uncertainty (“statistical sensitivity analysis”).

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Asymptotic solutions of differential equations and their applications by Calvin H. Wilcox

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