Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 305 -- 332

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This work is licensed under a Creative Commons Attribution 4.0 International License.

NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS USING DAUBECHIES FILTER WITH ACCURACY ORDER SIX

Athira Babu and Noufal Asharaf

Abstract. This article considers the representation of differentiation operators using Daubechies wavelets to solve PDEs numerically. Derivative approximation using this compactly supported wavelets convert the action into a matrix multiplication. The vanishing moments, dilation equation and quadrature formulas play a significant role in the scheme. The computed solution of the PDEs seems to behave better than the results reported in the literature, and we could progress the solution up to a large time-bound. We experimented with Daubechies wavelet filters with six vanishing moments on test problems and summarised the results.

2020 Mathematics Subject Classification: 65M22; 35L10
Keywords: Daubechies wavelet; Differentiation operator; Burgers' equation; Telegraph equation

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Athira Babu
Cochin University of Science and Technology
Kerala-682022, India.



Noufal Asharaf
Cochin University of Science and Technology
Kerala-682022, India.
e-mail: noufal@cusat.ac.in
Dr. Noufal Asharaf


http://www.utgjiu.ro/math/sma