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.
Kasnazani, A. and AliPanah, A. (2021). Solving brachistochrone problem via scaling functions of Daubechies wavelets. Computational Methods for Differential Equations, 9(2), 511-522. doi: 10.22034/cmde.2020.34778.1588
MLA
Kasnazani, A. , and AliPanah, A. . "Solving brachistochrone problem via scaling functions of Daubechies wavelets", Computational Methods for Differential Equations, 9, 2, 2021, 511-522. doi: 10.22034/cmde.2020.34778.1588
HARVARD
Kasnazani, A., AliPanah, A. (2021). 'Solving brachistochrone problem via scaling functions of Daubechies wavelets', Computational Methods for Differential Equations, 9(2), pp. 511-522. doi: 10.22034/cmde.2020.34778.1588
CHICAGO
A. Kasnazani and A. AliPanah, "Solving brachistochrone problem via scaling functions of Daubechies wavelets," Computational Methods for Differential Equations, 9 2 (2021): 511-522, doi: 10.22034/cmde.2020.34778.1588
VANCOUVER
Kasnazani, A., AliPanah, A. Solving brachistochrone problem via scaling functions of Daubechies wavelets. Computational Methods for Differential Equations, 2021; 9(2): 511-522. doi: 10.22034/cmde.2020.34778.1588
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