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

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Abstract

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 \(L_{\infty }\) 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.

Keywords

Two-dimensional Haar wavelets Two-dimensional reaction–subdiffusion Fractional two-dimensional problem Numerical solution 

Mathematics Subject Classification

65T60 65M70 35R11 

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Eğil Vocational and Technical Anatolian High SchoolDiyarbakirTurkey
  2. 2.Department of Mathematics, Faculty of Arts and ScienceInönü UniversityMalatyaTurkey
  3. 3.Department of Physics, Faculty of Arts and ScienceInönü UniversityMalatyaTurkey

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