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Finite differences for higher order derivatives of low resolution data

Author

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  • Balakrishna, Subramaniam
  • Schultz, William W.

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.

Suggested Citation

  • Balakrishna, Subramaniam & Schultz, William W., 2021. "Finite differences for higher order derivatives of low resolution data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 714-722.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:714-722
    DOI: 10.1016/j.matcom.2021.06.011
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