Solving the partial differential equation of vibrations with interval parameters using the interval finite difference method

Brenda G Medina, University of Texas at El Paso

Abstract

Accuracy and efficiency are among the main factors that drive today's innovative disciplines. As technology rapidly advances, efficiency takes on new meanings but what about accuracy? How accurate is accurate? Human error, uncertainties in measurement, and rounding errors are just some causes of inaccuracy. Interval Computations is an area that allows for such issues to be taken into account; for each measurement attained (for example), an interval can be built by considering the error associated with the measurement, and such an interval can be utilized in the mathematical computations of interest. ^ We consider the partial differential equation (PDE) of vibrations which has many applications in structural mechanics including modeling structures such as bridges, towers and other buildings. Converting the PDE of vibrations into an interval-parametrized equation, and applying interval computation techniques to accurately and efficiently find a solution would be of great value to the Engineering community. ^ In this work, we present the application of the interval finite difference method towards solving an interval-parametrized equation of dynamics, and we verify the efficiency and accuracy of the approach.^

Subject Area

Applied Mechanics|Applied Mathematics

Recommended Citation

Medina, Brenda G, "Solving the partial differential equation of vibrations with interval parameters using the interval finite difference method" (2011). ETD Collection for University of Texas, El Paso. AAI1503736.
http://digitalcommons.utep.edu/dissertations/AAI1503736

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