The New Laplace Transform: Closed-form Solutions and Applications in Gas Dynamics
N. S. Alharthi, R. E. Tolba · Research Square · 2023
Abstract This paper presents an investigation into finding the closed-form solution for a physical system in gas dynamics (GD), which is described by a set of partial differential equations (PDEs). The methodology employed involves utilising Laplace transforms to convert these complex equations into simpler ordinary differential equations (ODEs). In this study, we introduce the incorporation of first-order and second-order Bessel functions within Laplace transforms. Through our approach, we demonstrate that this method accurately solves ODEs and provides insights into various physical and engineering phenomena. The results obtained provide compelling evidence that Laplace transforms offer an effective way to obtain accurate solutions to ODEs, thereby enhancing our understanding of mathematical principles underlying diverse physical systems. Furthermore, these novel transformations hold promise for applications in engineering mathematics and mathematical physics computer programs. Specifically , this study highlights their potential relevance in investigating electron and ion movement within space plasma environments such as Titan-one of Sat-urn’s moons-as well as explaining electron escape from its atmosphere. These findings contribute valuable knowledge towards advancing our comprehension of gas dynamics phenomena while paving the way for future developments in computational modelling.