‎Solving brachistochrone problem via scaling functions of Daubechies wavelets

Document Type : Research Paper


Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.


In this paper, we proposed an effective method based on the scaling function of Daubechies wavelets for the solution of the brachistochrone problem. An analytic technique for solving the integral of Daubechies scaling functions on dyadic intervals is investigated and these integrals are used to reduce the brachistochrone problem into algebraic equations. The error estimate for the brachistochrone problem is proposed and the numerical results are given to verify the effectiveness of our method.


Volume 9, Issue 2
April 2021
Pages 511-522
  • Receive Date: 22 July 2019
  • Revise Date: 25 February 2020
  • Accept Date: 08 March 2020
  • First Publish Date: 01 April 2021