A MUNTZ-LEGENDRE APPROACH TO OBTAIN SOLUTIONS OF SINGULAR PERTURBED PROBLEMS

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YÜZBAŞI Ş., Gök E., Sezer M.

JOURNAL OF SCIENCE AND ARTS, sa.3, ss.537-544, 2020 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2020
  • Doi Numarası: 10.46939/j.sci.arts-20.3-a04
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.537-544
  • Anahtar Kelimeler: singular perturbed differential equations, Muntz-Legendre polynomials, collocation method, COLLOCATION METHOD, NUMERICAL-METHOD
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Singularly perturbed differential equations are encountered in mathematical modelling of processes in physics and engineering. Aim of this study is to give a collocation approach for solutions of singularly perturbed two-point boundary value problems. The method provides obtaining the approximate solutions in the form of Muntz-Legendre polynomials by using collocation points and matrix relations. Singularly perturbed problem is transformed into a system of linear algebraic equations. By solving this system, the approximate solution is computed. Also, an error estimation is done using the residual function and the approximate solutions are improved by means of the estimated error function. Two numerical examples are given to show the applicability of the method.