A collocation approach to solving the model of pollution for a system of lakes

YÜZBAŞI Ş., Sahin N., Sezer M.

MATHEMATICAL AND COMPUTER MODELLING, cilt.55, sa.3-4, ss.330-341, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 55 Sayı: 3-4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.mcm.2011.08.007
  • Dergi Adı: MATHEMATICAL AND COMPUTER MODELLING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.330-341
  • Anahtar Kelimeler: Modeling the pollution of a system of lakes, Collocation method, Collocation points, Bessel polynomials and series, Approximate solutions, FREDHOLM INTEGRODIFFERENTIAL EQUATIONS, CHEBYSHEV POLYNOMIAL SOLUTIONS, LINEAR-DIFFERENTIAL EQUATIONS, VARIABLE-COEFFICIENTS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. In this paper, the pollution problem of three lakes with interconnecting channels has been studied. A collocation method is presented to solve modeling the pollution of a system of lakes by a system of differential equations. By using Bessel polynomials and collocation points, this method transforms modeling the pollution of a system of lakes into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. A numerical example is included to demonstrate the validity and applicability of the technique. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB. (C) 2011 Elsevier Ltd. All rights reserved.