A numerical solution of the urysohn-type Fredholm integral equations

Jafarian A., Measoomy S., Khalili Golmankhaneh A., Baleanu D.

Romanian Journal of Physics, vol.59, no.7-8, pp.625-635, 2014 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 7-8
  • Publication Date: 2014
  • Journal Name: Romanian Journal of Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.625-635
  • Keywords: Approximate solution, Artificial neural networks approach, Bernstein polynomials method, Urysohn-type Fredholm integral equation
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In the present paper, a combination of the Bernstein polynomials and artificial neural networks (ANNs) is presented for solving the non-linear Urysohn equation. These polynomials are utilized to reduce the solution of the given problem to the solution of a system of non-linear algebraic equations. The remaining set of nonlinear equations is solved numerically by using the ANNs approach to yield truncated Bernstein series coefficients of the solution function. Several illustrative examples with numerical simulations are provided to support the theoretical claims.