A collocation approach for solving linear complex differential equations in rectangular domains

YÜZBAŞI Ş., Sahin N., Sezer M.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.35, sa.10, ss.1126-1139, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 10
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1002/mma.1590
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1126-1139
  • Anahtar Kelimeler: complex differential equations, collocation method, collocation points, approximate solution, Bessel polynomials and series, FREDHOLM INTEGRODIFFERENTIAL EQUATIONS, POLYNOMIAL SOLUTIONS, VARIABLE-COEFFICIENTS, APPROXIMATE SOLUTION, ANALYTIC-FUNCTIONS, OSCILLATION, SYSTEMS, PLANE
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, a collocation method is presented to find the approximate solution of high-order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, 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. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a). Copyright (c) 2012 John Wiley & Sons, Ltd.

In this paper, a collocation method is presented to find the approximate solution of high-order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, 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. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a).