Acoustic Field in Ducts With Sinusoidal Area Variation

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
N. S. Vikramaditya ◽  
R. B. Kaligatla
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Acoustic Field ◽  
Second Order ◽  
Ordinary Linear Differential Equation ◽  
Order Partial Differential Equation ◽  
Mean Flow ◽  
Area Variation ◽  
The Mean ◽  
Linear Differential

The purpose of this article is to provide an analytical solution for the acoustic field in a duct with sinusoidal area variation along the length. The equation describing the acoustic field in a variable area duct is a second-order partial differential equation. It is converted into a second-order ordinary linear differential equation, whose solution is dependent on the choice of area variation. The solution for the differential equation is obtained in terms of the area and is obtained neglecting the mean flow. Therefore, it is applicable in the absence of mean flow or in cases where the effects of mean flow are insignificant.

On a Linear Partial Differential Equation of Hyperbolic Type

1922 ◽  
Vol 41 ◽  
pp. 76-81
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Order Partial Differential Equation ◽  
Sound Waves ◽  
Partial Differential ◽  
Method Of Solution ◽  
Image Position

Riemann's method of solution of a linear second order partial differential equation of hyperbolic type was introduced in his memoir on sound waves. It has been used by Darboux in discussing the equationwhere α, β, γ are functions of x and y.

scholarly journals A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yin-shan Yun ◽  
Ying Wen ◽  
Temuer Chaolu ◽  
Randolph Rach
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Groundwater Flow ◽  
Boundary Value ◽  
Flow Region ◽  
Second Order ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Adomian Decomposition

Abstract For the boundary value problem (BVP) of a second-order partial differential equation on a plane triangle area, we propose a new algorithm based on the Adomian decomposition method (ADM) combined with a segmented technique. In addition, we present a new theorem that ensures the convergence of the algorithm. By this algorithm, the model for the effect of regional recharge on the plane triangle groundwater flow region is solved, from which we obtain the segmented exact solution of the problem, which satisfies the governing equation and all of the specified boundary conditions. Then, by the algorithm combined with Taylor’s formula, the heterogeneous aquifer model on the plane triangle groundwater flow region is considered, from which we obtain the segmented high-precision approximate solution of the problem.

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