Lossless propagation of one-dimensional, finite amplitude sound waves

Banta, E.

doi:10.1016/0022-247x(65)90153-8

Cited by 14 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consider the nonlinear shock wave fractal model such as with the initial condition where γ is the specific heat, c 0 and γ are constants. In [ 32 ], it is shown that if then a series solution yield as where and H n (.) is the Hermit polynomial of order n .…”

Section: Numerical Examplesmentioning

confidence: 99%

An efficient scheme for nonlinear shock wave model in a fractal domain under Caputo fractional operator

Nadeem,

Alsayaad

2024

PLoS ONE

View full text Add to dashboard Cite

This paper introduces a refined approach for obtaining the analytical solution of the nonlinear shock wave model incorporating fractal derivatives. The Fractal Yang Variational Iteration Strategy (FYVIS) is utilized to obtain the approximate solution of a fractal model in the form of a series under Caputo fractional operator. The suggested method is the composition of the fractal Yang transform and the variational iteration approach. By using the two-scale fractal theory, we transform the fractal model into its traditional problem and then apply the yang transform to generate a recurrence relation. The variational iteration approach is now suitable to handle this recurrence relation without imposing any hypotheses or restrictions on variables. The derived results by the proposed scheme are shown in terms of series solution. Numerical calculations verify the accuracy and consistency of the suggested approach, demonstrating its excellent performance. The dynamic behavior of fractal components is explored by evaluating absolute errors and presenting two-dimensional diagrams across the fractal domain. This investigation underscores that the suggested technique offers an efficient and user-friendly solution for solving the nonlinear shock wave model involving fractal derivatives.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

An efficient scheme for nonlinear shock wave model in a fractal domain under Caputo fractional operator

Nadeem,

Alsayaad

2024

PLoS ONE

View full text Add to dashboard Cite

show abstract

The propagation of magnetohydrodynamic simple waves

Gundersen

1966

Journal of Applied Mathematics and Physics (ZAMP)

View full text Add to dashboard Cite

Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics

Zhang

Sheng

2006

Appl. Math. Chin. Univ.

View full text Add to dashboard Cite

The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given. w 1 IntroductionIn the present paper,we are interested in solving the Cauchy problem for linearized system of two-dimensional isentropic flow with initial data in gas dynamics2) where p is the density, (u,v) is the velocity, po is a positive eonstant,p=p(p) is the equation of state satisfying p~ (p0)>0, (r,O) is the polar coordinate such that X ~ rcosO~ y rsin0, 0~r~+ oo, 0~0~ 2zr, (1.3)and P0 (r), u0 (r), v0 (r) are bounded piecewise smooth functions. In fact ,system (1.1) is also a system of sound waves. The characteristic of sound field can be described by sound pressure in medium, velocity of particles and density. By the physical course of sound waves, we can see that the variations of pressure, velocity and density are correlated in the course of sound perturbation. Therefore we must find the relationship among them. As a macroscopic physical phenomenon,it is necessary that the

show abstract

Lossless propagation of one-dimensional, finite amplitude sound waves

Cited by 14 publications

References 4 publications

An efficient scheme for nonlinear shock wave model in a fractal domain under Caputo fractional operator

An efficient scheme for nonlinear shock wave model in a fractal domain under Caputo fractional operator

The propagation of magnetohydrodynamic simple waves

Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics

Contact Info

Product

Resources

About