Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets

Jokar M., Lakestanı M.

Kybernetika, cilt.48, sa.5, ss.939-957, 2012 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 5
  • Basım Tarihi: 2012
  • Dergi Adı: Kybernetika
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.939-957
  • Anahtar Kelimeler: Hermite interpolation, Operational matrix of derivative, Telegraph equation, Trigonometric wavelets
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate results. An estimation of error bound for this method is presented and it is shown that in this method the matrix of coefficients is a sparse matrix.