Abstract

We present a numerical method for the solution of Newton's problem of least resistance in the class of convex functions using a convex hull approach. We observe that the numerically computed solutions possess some symmetry. Further, their extremal points lie on several curves. By exploiting this conjectured structure, we are able to compute highly accurate solutions to Newton's problem.

Author information

Contact details are reproduced from the original publication and may be historical.

Gerd Wachsmuth

Brandenburgische Technische Universität Cottbus-Senftenberg Institute of Mathematics, Cottbus, Germany

gerd.wachsmuth@b-tu.de

Keywords

  • Newton's problem of minimal resistance
  • convex hull
  • calculus of variations with convexity constraint

Mathematics Subject Classification

49Q10, 52A15, 52A40

Suggested citation

G. Wachsmuth. “New Numerical Solutions to Newton's Problem of Least Resistance via a Convex Hull Approach.” Journal of Convex Analysis 34 (2027), No. 1, 610–617. https://doi.org/10.68381/jca34041

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