A collocation method to find solutions of linear complex differential equations in circular domains

YÜZBAŞI Ş., Sezer M.

APPLIED MATHEMATICS AND COMPUTATION, cilt.219, sa.22, ss.10610-10626, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 219 Sayı: 22
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.amc.2013.03.056
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.10610-10626
  • Anahtar Kelimeler: Complex differential equations, Bessel functions of the first kind, Collocation method, Collocation points, Approximate solution, Numerical solution, APPROXIMATE SOLUTION, POLYNOMIAL SOLUTIONS, COEFFICIENTS, OSCILLATION, SYSTEMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, we introduce a collocation approach for solving high-order linear complex differential equations in circular domain. By using collocation points defined in a circular domain and Bessel functions of the first kind, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. Proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are given to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results obtained from the examples demonstrate the efficiency and accuracy of the present work. All of the numerical computations have been computed on computer using a code written in Matlab. (C) 2013 Elsevier Inc. All rights reserved.