Numerical solutions of system of linear Fredholm-Volterra integro-differential equations by the Bessel collocation method and error estimation

Yuzbasi S.

APPLIED MATHEMATICS AND COMPUTATION, cilt.250, ss.320-338, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 250
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1016/j.amc.2014.10.110
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.320-338
  • Anahtar Kelimeler: System of Fredholm-Volterra integro differential equations, The Bessel functions of first kind, The Bessel collocation method, Collocation points, Residual error estimation, INTEGRAL-EQUATIONS, TAU METHOD, MODEL
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, the Bessel collocation method is presented for the solutions of system of linear Fredholm-Volterra integro-differential equations which includes the derivatives of unknown functions in integral parts. The Bessel collocation method transforms the problem into a system of linear algebraic equations by means of the Bessel functions of first kind, the collocation points and the matrix relations. Also, an error estimation is given for the considered problem and the method. Illustrative examples are presented to show efficiency of method and the comparisons are made with the results of other methods. All of numerical calculations have been made on a computer using a program written in Matlab. (C) 2014 Elsevier Inc. All rights reserved.

In this study, the Bessel collocation method is presented for the solutions of system of linear Fredholm–Volterra integro-differential equations which includes the derivatives of unknown functions in integral parts. The Bessel collocation method transforms the problem into a system of linear algebraic equations by means of the Bessel functions of first kind, the collocation points and the matrix relations. Also, an error estimation is given for the considered problem and the method. Illustrative examples are presented to show efficiency of method and the comparisons are made with the results of other methods. All of numerical calculations have been made on a computer using a program written in Matlab.