A solution for reducing the degree of polynomial composition functions using Faà di Bruno’s formula and Fourier transform

Ahani E., Ahani A.

Boletin de la Sociedad Matematica Mexicana, vol.29, no.2, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s40590-023-00521-3
  • Journal Name: Boletin de la Sociedad Matematica Mexicana
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Bell’s polynomial, Degree reduction, Faà di Bruno’s formula, Fourier transform
  • Istanbul Technical University Affiliated: Yes


Various studies concerning reducing the degree of order for nonlinear differential equations have been carried out. Yet, reducing the specified degree and a solution for them is a matter of discussion. In this study, based on Faà di Bruno’s formula and using Fourier transform, a general method for reducing the degree of the equation to the desired degree has proposed. To appraise the efficacy of the proffered method, the function of the nth degree of polynomial composition function has been reduced by one and to one at the ending. The provided solution could have some uses in solving the high order differential equations of high degrees, which is practical for applied mathematics and engineering problems. The concept may implement to reduce the complexity of differential equations of higher order to more compatible forms of mathematical equations with acquirable solutions. The outcomes could be used for solving nonlinear differential equations of any order, especially those related to nonlinear engineering problems computational mechanics.