<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we develop a precise and efficient ultraspherical wavelet method for a famous Benjamin-Bona-Mahony (BBM) mathematical model. The suggested technique uses the collocation method and ultraspherical wavelets. The proposed scheme is applied to linear and nonlinear BBM equations to inspect the efficiency and accuracy of the proposed technique. The effectiveness of this practical approach is verified. Moreover, the method based on the ultraspherical wavelets is simple, accurate, fast, flexible, and convenient. The results are analyzed using tables and graphs and compared with other methods in literature. As we know, many partial differential equations (PDEs) don’t have exact solutions, and some semi-analytical methods work based on controlling parameters, but this is a controlling parameter-free technique. Also, it is pretty simple to implement and consumes less time to execute the programs. The recommended wavelet-based numerical approach is interesting, productive, and efficient. The proposed technique's convergence analysis is also presented through the theorem.</p>
</abstract>

In this paper, we develop a precise and efficient ultraspherical wavelet method for a famous Benjamin-Bona-Mahony (BBM) mathematical model. The suggested technique uses the collocation method and ultraspherical wavelets. The proposed scheme is applied to linear and nonlinear BBM equations to inspect the efficiency and accuracy of the proposed technique. The effectiveness of this practical approach is verified. Moreover, the method based on the ultraspherical wavelets is simple, accurate, fast, flexible, and convenient. The results are analyzed using tables and graphs and compared with other methods in literature. As we know, many partial differential equations (PDEs) don’t have exact solutions, and some semi-analytical methods work based on controlling parameters, but this is a controlling parameter-free technique. Also, it is pretty simple to implement and consumes less time to execute the programs. The recommended wavelet-based numerical approach is interesting, productive, and efficient. The proposed technique's convergence analysis is also presented through the theorem.

A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this paper, we develop a precise and efficient ultraspherical wavelet method for a famous Benjamin-Bona-Mahony (BBM) mathematical model. The suggested...

A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method

Article Category: Original Study

Published Online: Jan 10, 2024

Page range: 179 - 192

Received: Jul 27, 2023

Accepted: Sep 06, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0014

Keywords
Benjamin-Bona-Mahony equation, ultraspherical wavelet, collocation method

© 2024 Mallanagoud Mulimani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method

Article Category: Original Study

Published Online: Jan 10, 2024

Page range: 179 - 192

Received: Jul 27, 2023

Accepted: Sep 06, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0014

KeywordsBenjamin-Bona-Mahony equation, ultraspherical wavelet, collocation method

© 2024 Mallanagoud Mulimani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Benjamin-Bona-Mahony equation, ultraspherical wavelet, collocation method