A Bernoulli polynomial approach with residual correction for solving mixed linear Fredholm integro-differential-difference equations

Erdem K., Yalçinbaş S., Sezer M.

Journal of Difference Equations and Applications, cilt.19, sa.10, ss.1619-1631, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 10
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1080/10236198.2013.768619
  • Dergi Adı: Journal of Difference Equations and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1619-1631
  • Anahtar Kelimeler: Bernoulli polynomials, linear Fredholm integro-differential-difference equations, Bernoulli matrix method, collocation points
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, an approximate method based on Bernoulli polynomials and collocation points has been presented to obtain the solution of higher order linear Fredholm integro-differential-difference equations with the mixed conditions. The method we have used consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on the matrix forms of Bernoulli polynomials and their derivatives by means of collocations. The solutions are obtained as the truncated Bernoulli series which are defined in the interval [a,b]. To illustrate the method, it is applied to the initial and boundary values. Also error analysis and numerical examples are included to demonstrate the validity and applicability of the technique. © 2013 Copyright Taylor and Francis Group, LLC.