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

<p>In this article, we propose a technique based on modified double integral transforms used to solve certain equations of materials science, namely Benney–Luke (BL) and singular pseudo-hyperbolic (SP-H) equations. We have established some analytical results. This method can provide accurate one-step solutions, although the equations used may exhibit a singularity in the initial conditions. Some numerical examples have been discussed for illustration and to show the effectiveness of the technique for certain types of equations. We have developed an exact solution in just one step, whereas other approaches require several stages to succeed in a particular solution, making the proposed strategy particularly successful and straightforward to apply to various varieties of the B–L and SP-H equations.</p>
</abstract>

In this article, we propose a technique based on modified double integral transforms used to solve certain equations of materials science, namely Benney–Luke (BL) and singular pseudo-hyperbolic (SP-H) equations. We have established some analytical results. This method can provide accurate one-step solutions, although the equations used may exhibit a singularity in the initial conditions. Some numerical examples have been discussed for illustration and to show the effectiveness of the technique for certain types of equations. We have developed an exact solution in just one step, whereas other approaches require several stages to succeed in a particular solution, making the proposed strategy particularly successful and straightforward to apply to various varieties of the B–L and SP-H equations.

Modified Integral Transform for Solving Benney-Luke and Singular Pseudo-Hyperbolic Equations

Mathematics Department, College of Sciences and Arts

Department of Mathematic, Faculty of Sciences and Arts

Acta Mechanica et Automatica

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

In this article, we propose a technique based on modified double integral transforms used to solve certain equations of materials science, namely Benney–Luke...

Modified Integral Transform for Solving Benney-Luke and Singular Pseudo-Hyperbolic Equations

Published Online: Feb 29, 2024

Page range: 139 - 143

Received: Feb 08, 2023

Accepted: Aug 20, 2023

DOI: https://doi.org/10.2478/ama-2024-0018

Keywords
convergence, pseudo-hyperbolic equation, Benney–Luke equation

© 2024 Tarig M. Elzaki et al., published by Sciendo

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

Modified Integral Transform for Solving Benney-Luke and Singular Pseudo-Hyperbolic Equations

Published Online: Feb 29, 2024

Page range: 139 - 143

Received: Feb 08, 2023

Accepted: Aug 20, 2023

DOI: https://doi.org/10.2478/ama-2024-0018

Keywordsconvergence, pseudo-hyperbolic equation, Benney–Luke equation

© 2024 Tarig M. Elzaki et al., published by Sciendo

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

Keywords
convergence, pseudo-hyperbolic equation, Benney–Luke equation