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

• Published in: Engineering computations Vol. 38; no. 4; pp. 1706 - 1724
• Main Authors: Pandit, Sapna, Mittal, R.C
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 17-06-2021; Emerald Group Publishing Limited
• Subjects: Advection; Algorithms; Approximation; Boundary conditions; Computational fluid dynamics; Data compression; Error analysis; Finite element analysis; Fourier transforms; Gaussian elimination; Numerical analysis; Partial differential equations; Porous media; Unsteady state; Uniform scale-3 Haar wavelets; Collocation points; Space fractional advection dispersion equation
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-01-2020-0013

Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.