Solving differential equations by wavelet transform method based on the mother wavelets & differential invariants

HAMID REZA YAZDANI; MEHDI NADJAFIKHAH; MEGERDICH TOOMANIAN

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Solving differential equations by wavelet transform method based on the mother wavelets & differential invariants

Author(s)

HAMID REZA YAZDANI Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran; School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran; Department of Mathematics, Karaj Branch Islamic Azad University, Karaj, Iran.

MEHDI NADJAFIKHAH Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran; School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran; Department of Mathematics, Karaj Branch Islamic Azad University, Karaj, Iran.

MEGERDICH TOOMANIAN Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran; School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran; Department of Mathematics, Karaj Branch Islamic Azad University, Karaj, Iran.

Abstract

Nowadays, wavelets have been widely used in various elds of science and technology. Meanwhile, the wavelet transforms and the generation of new Mother wavelets are noteworthy. In this paper, we generate new Mother wavelets and analyze the differential equations by using of their corresponding wavelet transforms. This method by Mother wavelets and the corresponding wavelet transforms produces analytical solutions for PDEs and ODEs.

Publication Details

Page(s) 74-86

DOI DOI not available

Published Journal: Journal of Prime Research in Mathematics, Volume: 14, Issue: 1, Year: 2018

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Keywords

wavelet transform, Wavelet, 76M60, Mother wavelet, Differential invariant, Degree reduction AMS SUBJECT, 42C40, 65T60, 54H15

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