A collocation method based on Bernstein polynomials to solve nonlinear Fredholm-Volterra integro-differential equations

YÜZBAŞI Ş.

APPLIED MATHEMATICS AND COMPUTATION, cilt.273, ss.142-154, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 273
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.amc.2015.09.091
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.142-154
  • Anahtar Kelimeler: Nonlinear integro-differential equations, Bernstein polynomials, Collocation method, Bernstein series method, Approximate solution, NUMERICAL-SOLUTION, INTEGRAL-EQUATIONS, DIFFERENTIAL-EQUATIONS, SERIES SOLUTION, TAU METHOD, SYSTEMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, a collocation method that based on Bernstein polynomials is presented for nonlinear Fredholm-Volterra integro-differential equations (NFVIDEs). By means of the collocation method and the matrix operations, the problem is reduced into a system of the nonlinear algebraic equations. The approximate solutions are obtained by solving this nonlinear system. Error analysis is presented for the Bernstein series solutions of the nonlinear Fredholm-Volterra integro-differential equations. Several examples are given to illustrate the efficiency and implementation of the proposed method for solving the NFVIDEs. Comparisons are made to confirm the reliability of the method. Also error analysis is applied for the numerical examples. (C) 2015 Elsevier Inc. All rights reserved.