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

Hamid Reza Yazdani
Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran.
Mehdi Nadjafikhah
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
Megerdich Toomanian
Department of Mathematics, Karaj Branch Islamic Azad University, Karaj, Iran.

\(^{1}\)Corresponding Author: yazdani@phd.pnu.ac.ir

Copyright © 2018 Hamid Reza Yazdani, Mehdi Nadjafikhah, Megerdich Toomanian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2018.

Abstract

Nowadays, wavelets have been widely used in various fields 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.

Keywords:

Wavelet, Mother wavelet, Wavelet transform, Differential invariant, Degree reduction.