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A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation

Sapna Pandit (Department of Mathematics and Statistics, Gurukul Kangri Vishwavidyalaya, Haridwar, India)
R.C. Mittal (Jaypee Institute of Information Technology, Noida, India)

Engineering Computations

ISSN: 0264-4401

Article publication date: 20 October 2020

Issue publication date: 17 June 2021




This paper aims to propose a novel approach based on uniform scale-3 Haar wavelets for unsteady state space fractional advection-dispersion partial differential equation which arises in complex network, fluid dynamics in porous media, biology, chemistry and biochemistry, electrode – electrolyte polarization, finance, system control, etc.


Scale-3 Haar wavelets are used to approximate the space and time variables. Scale-3 Haar wavelets converts the problems into linear system. After that Gauss elimination is used to find the wavelet coefficients.


A novel algorithm based on Haar wavelet for two-dimensional fractional partial differential equations is established. Error estimation has been derived by use of property of compactly supported orthonormality. The correctness and effectiveness of the theoretical arguments by numerical tests are confirmed.


Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.



The work is supported by University Grant Commission (UGC) under the D. S. Kothari Postdoctoral Fellowship scheme with grant No. MA/18-19/0013.


Pandit, S. and Mittal, R.C. (2021), "A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation", Engineering Computations, Vol. 38 No. 4, pp. 1706-1724.



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