Numerical solution of partial differential equations using Daubechies Filter with accuracy order six
his 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 formula...
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Published in | Surveys in mathematics and its applications Vol. 17 (2022); pp. 305 - 332 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
University Constantin Brancusi of Targu-Jiu
01.08.2022
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Subjects | |
Online Access | Get full text |
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Summary: | his 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. |
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ISSN: | 1843-7265 1842-6298 |