Numerical simulation of fractional-order two-dimensional Helmholtz equations-Reference-Cited by-同舟云学术

Numerical simulation of fractional-order two-dimensional Helmholtz equations

Published:2023 Issue:6 Volume:8 Page:13205-13218
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Iqbal Naveed¹,Chughtai Muhammad Tajammal²,Shah Nehad Ali³

Affiliation:

1. Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia

2. Department of Electrical Engineering, College of Engineering, University of Ha'il, Ha'il 55427, Saudi Arabia

3. Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea

Abstract

<abstract><p>In this paper, we investigate the exact solutions of several fractional-order Helmholtz equations using the homotopy perturbation transform method. We specify sufficient requirements for its convergence and provide error estimations. The homotopy perturbation transform method yields a quickly converging succession of solutions. Solutions for various fractional space derivatives are compared to present approaches and explained using figures. Appropriate parameter selection produces approximations identical to the exact answer. Test examples are provided to demonstrate the proposed approach's precision and competence. The results demonstrate that our system is appealing, user-friendly, dependable, and highly effective.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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