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

F. Bulut1,2, Ö. Oruç3, A. Esen3
İnonu University, Department of Physics, Malatya, TURKEY.
Corresponding author: E-mail: fatih.bulut@inonu.edu.tr Tel: +904223773745, Fax: +904223410037.
İnonu University, Department of Mathematics, Malatya, TURKEY.

Computer Modeling in Engineering & Sciences 2015, 108(4), 263-284. https://doi.org/10.3970/cmes.2015.108.263

Abstract

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. L2 and L 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.

Keywords

Haar wavelet method, Fractional coupled KdV equation, Fractional coupled MKdV equation, Linearization, Numerical solution.

Cite This Article

Bulut, F., Oruç, ., Esen, A. (2015). Numerical Solutions of Fractional System of Partial Differential Equations By Haar Wavelets. CMES-Computer Modeling in Engineering & Sciences, 108(4), 263–284.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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