A Bessel polynomial approach for solving general linear Fredholm integro-differential-difference equations

Sahin N., YÜZBAŞI Ş., Sezer M.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.88, sa.14, ss.3093-3111, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 88 Sayı: 14
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1080/00207160.2011.584973
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3093-3111
  • Anahtar Kelimeler: Fredholm integro-differential-difference equations, the Bessel polynomials and series, the Bessel matrix method, collocation points, NUMERICAL-SOLUTION, INTEGRODIFFERENTIAL EQUATIONS, APPROXIMATE SOLUTION, TAYLOR, ALGORITHM, TERMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, to find an approximate solution of general linear Fredholm integro-differential-difference equations (FIDDEs) under the initial-boundary conditions in terms of the Bessel polynomials, a practical matrix method is presented. The idea behind the method is that it converts FIDDEs to a matrix equation which corresponds to a system of linear algebraic equations and is based on the matrix forms of the Bessel polynomials and their derivatives by means of collocation points. The solutions are obtained as the truncated Bessel series in terms of the Bessel polynomials J(n)(x) of the first kind defined in the interval [0, infinity). The error analysis and the numerical examples are included to demonstrate the validity and applicability of the technique.