A collocation approach for solving a class of complex differential equations in elliptic domains

YÜZBAŞI Ş., Sahin N., Gulsu M.

JOURNAL OF NUMERICAL MATHEMATICS, cilt.19, sa.3, ss.225-246, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 3
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1515/jnum.2011.011
  • Dergi Adı: JOURNAL OF NUMERICAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.225-246
  • Anahtar Kelimeler: complex differential equations, collocation method, collocation points, approximate solution, Bessel polynomials and series, POLYNOMIAL SOLUTIONS, APPROXIMATE SOLUTION, OSCILLATION, SYSTEMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, a numerical method is developed to compute an approximate solution of high-order linear complex differential equations in elliptic domains. By using collocation points and Bessel polynomials, this method transforms the linear complex differential equation into a matrix equation which corresponds to a system of linear equations in the unknown Bessel coefficients. The suggested method reproduces the analytic solution when it is polynomial. Some numerical examples are given to illustrate the applicability and validity of the technique and comparisons are made with other existing approaches.