A Laguerre Approach for the Solutions of Singular Perturbated Differential Equations

YÜZBAŞI Ş.

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, cilt.14, sa.4, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219876217500347
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Singular perturbated differential equations, boundary value problems, laguerre polynomials, collocation scheme, collocation points, residual correction, NUMERICAL-SIMULATION, COLLOCATION METHOD, ALGORITHM, SCHEME
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, a Laguerre method is presented to solve singularly perturbated two-point boundary value problems. By means of the matrix relations of the Laguerre polynomials and their derivatives, original problem is transformed into a matrix equation. Later, we use collocation points in the matrix equation and thus the considered problem is reduced to a system of linear algebraic equations. The solution of this system gives the coefficients of the desired approximate solution. Also, an error estimation based on the residual function is introduced for the method. The Laguerre polynomial solution is improved by using this error estimation. Finally, error estimation and residual improvement are illustrated by examples and comparisons are given with other methods.