A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers' equation

ORUC Ö., BULUT F., ESEN A.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.53, sa.7, ss.1592-1607, 2015 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 7
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s10910-015-0507-5
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1592-1607
  • Anahtar Kelimeler: Haar wavelet method, Modified Burgers' equation, Linearization, Finite differences, Numerical solution, COLLOCATION METHOD, 2D
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper, we investigate the numerical solutions of one dimensional modified Burgers' equation with the help of Haar wavelet method. In the solution process, the time derivative is discretized by finite difference, the nonlinear term is linearized by a linearization technique and the spatial discretization is made by Haar wavelets. The proposed method has been tested by three test problems. The obtained numerical results are compared with the exact ones and those already exist in the literature. Also, the calculated numerical solutions are drawn graphically. Computer simulations show that the presented method is computationally cheap, fast, reliable and quite good even in the case of small number of grid points.