A collocation approach to solve the Riccati-type differential equation systems

YÜZBAŞI Ş.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.89, sa.16, ss.2180-2197, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 89 Sayı: 16
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1080/00207160.2012.703777
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2180-2197
  • Anahtar Kelimeler: system of the Riccati-type differential equations, approximate solutions, collocation method, collocation points, Bessel functions of first kind, Bessel collocation method, ADOMIAN DECOMPOSITION METHOD, NUMERICAL-SOLUTION, HIV-INFECTION, INTEGRODIFFERENTIAL EQUATIONS, POLYNOMIAL SOLUTIONS, MODEL, DYNAMICS
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

In this paper, a collocation method is presented for the solutions of the system of the Riccati-type differential equations with variable coefficients. The proposed approach consists of reducing the problem to a nonlinear algebraic equation system by expanding the approximate solutions in terms of the Bessel polynomials with unknown coefficients. The unknown coefficients of the Bessel polynomials are found by using the matrix operations of derivatives together with the collocation method. The proposed method gives the analytic solutions when the exact solutions are polynomials. Also, an error analysis technique based on the residual function is introduced for the suggested method. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Comparing the methodology with some known techniques shows that the presented approach is relatively easy and highly accurate. All of the numerical calculations have been done by using a program written in Maple.

In this paper, a collocation method is presented for the solutions of the system of the Riccati-type differential equations with variable coefficients. The proposed approach consists of reducing the problem to a nonlinear algebraic equation system by expanding the approximate solutions in terms of the Bessel polynomials with unknown coefficients. The unknown coefficients of the Bessel polynomials are found by using the matrix operations of derivatives together with the collocation method. The proposed method gives the analytic solutions when the exact solutions are polynomials. Also, an error analysis technique based on the residual function is introduced for the suggested method. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Comparing the methodology with some known techniques shows that the presented approach is relatively easy and highly accurate. All of the numerical calculations have been done by using a program written in Maple.