Finite differences for higher order derivatives of low resolution data

Subramaniam Balakrishna and William W. Schultz

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 714-722

Abstract: The viability of finite difference stencils for higher-order derivatives of low-resolution data, encountered in various applications, is examined. This study’s illustrative example involves the evaluation of the fourth derivative of the digitized free surface radius obtained from pixelated images. Procedures to obtain an optimal approximation to the derivative are made from estimates of truncation and roundoff error, with emphasis on the analysis of roundoff error. A method of successive approximations to evaluate the optimal grid spacing is presented. Higher-order stencils allow for larger optimal grid spacing, thereby reducing the roundoff error that would otherwise dominate. Hence, higher-order stencils are effective for low precision data.

Keywords: Finite difference methods; Low resolution data; Higher order derivatives (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:714-722

DOI: 10.1016/j.matcom.2021.06.011

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