A haar wavelet approximation for two-dimensional time fractional reaction-subdiffusion equation

Oruc O., ESEN A., BULUT F.

ENGINEERING WITH COMPUTERS, cilt.35, sa.1, ss.75-86, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00366-018-0584-8
  • Dergi Adı: ENGINEERING WITH COMPUTERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.75-86
  • Anahtar Kelimeler: Two-dimensional Haar wavelets, Two-dimensional reaction-subdiffusion, Fractional two-dimensional problem, Numerical solution, PARTIAL-DIFFERENTIAL-EQUATIONS, NUMERICAL-SOLUTION, INTEGRAL-EQUATIONS, OPERATIONAL MATRIX, POISSON EQUATIONS, STATE ANALYSIS, DIFFUSION, SCHEME, COLLOCATION, SIMULATION
  • İnönü Üniversitesi Adresli: Evet

Özet

In this study, we established a wavelet method, based on Haar wavelets and finite difference scheme for two-dimensional time fractional reaction-subdiffusion equation. First by a finite difference approach, time fractional derivative which is defined in Riemann-Liouville sense is discretized. After time discretization, spatial variables are expanded to truncated Haar wavelet series, by doing so a fully discrete scheme obtained whose solution gives wavelet coefficients in wavelet series. Using these wavelet coefficients approximate solution constructed consecutively. Feasibility and accuracy of the proposed method is shown on three test problems by measuring error in norm. Further performance of the method is compared with other methods available in literature such as meshless-based methods and compact alternating direction implicit methods.