A shifted Legendre method for solving a population model and delay linear Volterra integro-differential equations

YÜZBAŞI Ş.

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, cilt.10, sa.7, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 7
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s1793524517500917
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIOMATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Population model, delay Volterra integro-differential equations, shifted Legendre polynomials, matrix method, collocation method, HOMOTOPY PERTURBATION METHOD, FREDHOLM INTEGRAL-EQUATIONS, RATIONALIZED HAAR FUNCTIONS, NUMERICAL-SOLUTION, DIFFERENTIAL-EQUATIONS, NONLINEAR-SYSTEMS, COLLOCATION, MATRIX
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we propose a collocation method to obtain the approximate solutions of a population model and the delay linear Volterra integro-differential equations. The method is based on the shifted Legendre polynomials. By using the required matrix operations and collocation points, the delay linear Fredholm integro-differential equation is transform ed info a matrix equation. The matrix equation corresponds to a system of linear algebraic equations. Also, an error estimation method for method and improvement of solutions is presented by using the residual function. Applications population of model and general delay integro-differential equation are given. T he obtained results are compared with the known results.