Numerical Solutions of Fractional System of Partial Differential Equations By HaarWavelets
F. Bulut, Ö. Oruç and A. Esen

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 108, No. 4, pp. 263-284, 2015
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Keywords Haar wavelet method, Fractional coupled KdV equation, Fractional coupled MKdV equation, Linearization, Numerical solution.

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.

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