Back to Search Start Over

A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation.

Authors :
Nadeem, Muhammad
Li, Zitian
Kumar, Devendra
Alsayaad, Yahya
Source :
Scientific Reports. 2/20/2024, Vol. 14 Issue 1, p1-13. 13p.
Publication Year :
2024

Abstract

The Helmholtz equation plays a crucial role in the study of wave propagation, underwater acoustics, and the behavior of waves in the ocean environment. The Helmholtz equation is also used to describe propagation through ocean waves, such as sound waves or electromagnetic waves. This paper presents the Elzaki transform residual power series method (E T-RPSM) for the analytical treatment of fractional-order Helmholtz equation. To develop this scheme, we combine Elzaki transform (E T) with residual power series method (RPSM). The fractional derivatives are described in Caputo sense. The E T is capable of handling the fractional order and turning the problem into a recurrence form, which is the novelty of our paper. We implement RPSM in such a way that this recurrence relation generates the results in the form of an iterative series. Two numerical applications are considered to demonstrate the efficiency and authenticity of this scheme. The obtained series are determined very quickly and converge to the exact solution only after a few iterations. Graphical plots and absolute error are shown to observe the authenticity of this suggested approach. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
20452322
Volume :
14
Issue :
1
Database :
Academic Search Index
Journal :
Scientific Reports
Publication Type :
Academic Journal
Accession number :
175832532
Full Text :
https://doi.org/10.1038/s41598-024-54870-8