Neelesh Kumar

Department of Mathematics, Dyal Singh College, University of Delhi, Lodhi Road, Pragati Vihar, New Delhi-110 003, India, E-mails: neeleshkr2012@gmail.com; neeleshkumar.maths@dsc.du.ac.in

Received in final form on June 21, 2023

Abstract
A highly accurate sixth-order compact finite difference scheme is proposed for the three-dimensional Helmholtz equation in a homogeneous medium. A hybrid scheme, a combination of two schemes, is also proposed for the Helmholtz equation. The proposed schemes are illustrated by four examples, the first two of which arise in acoustics, while the last two arise in electromagnetics. Numerical experiments demonstrate that the proposed schemes have very high accuracy in comparison to available schemes for the three-dimensional Helmholtz equation.

Keywords
Helmholtz Equation, High Order Compact Schemes, Hybrid Scheme.

Cite This Article
Neelesh Kumar, Highly Accurate Finite Difference Schemes for the Three-Dimensional Helmholtz Equation, J. Innovation Sciences and Sustainable Technologies, 3(3)(2023), 161 - 181. https://doie.org/10.0904/JISST.2023531643

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