NUMERICAL SOLUTIONS OF DIFFERENTIAL-ALGEBRAIC EQUATIONS (DAEs) USING LEGENDRE POLYNOMIALS APPROXIMATIONS

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AKAR M.

JOURNAL OF SCIENCE AND ARTS, sa.2, ss.449-458, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2022
  • Doi Numarası: 10.46939/j.sci.arts-22.2-a17
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.449-458
  • Anahtar Kelimeler: Legendre polynomials approximations, power series, differenti-alalgebraic equations (DAEs)
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, the Legendre polynomials approximations are studied for the numerical solutions of differential-algebraic equations (DAEs). An algorithm of the method constructed using Legendre polynomials approximations is developed to solve DAE systems. Two test problems are answered to illustrate the Legendre polynomials approximations, and then the obtained solutions are confronted with the exact solutions of the problems. As a first step, the power series of an allowed equation system is determined, in second step it is converted into Legendre polynomials approximations structure which allows an arbitrary order. Furthermore, to get numerical solution of DAEs with Legendre polynomials approximations, a Maple algorithm is implemented. Graphs of obtained solutions are sketched, and are created tables to compare the exact solutions by using Maple programming.