Numerical Solutions of Fractional System of Partial Differential Equations By Haar Wavelets

BULUT F., ORUC Ö., ESEN A.

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, cilt.108, sa.4, ss.263-284, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 108 Sayı: 4
  • Basım Tarihi: 2015
  • Dergi Adı: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.263-284
  • Anahtar Kelimeler: Haar wavelet method, Fractional coupled KdV equation, Fractional coupled MKdV equation, Linearization, Numerical solution, OPERATIONAL MATRIX, SOLITON-SOLUTIONS, DIFFUSION EQUATION, TRANSFORM METHOD, ORDER, SIMULATION
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper, time fractional one dimensional coupled KdV and coupled modified KdV equations are solved numerically by Haar wavelet method. Proposed method is new in the sense that it doesn't use fractional order Haar operational matrices. In the proposed method L1 discretization formula is used for time discretization where fractional derivatives are Caputo derivative and spatial discretization is made by Haar wavelets. L-2 and L-infinity error norms for various initial and boundary conditions are used for testing accuracy of the proposed method when exact solutions are known. Numerical results which produced by the proposed method for the problems under consideration confirm the feasibility of Haar wavelet method combined with L1 discretization formula.