APPLICATION OF A NUMERICAL-ANALYTICAL METHOD FOR SOLVING A ONE-DIMENSIONAL WAVE EQUATION

Akustika ◽  
2021 ◽  
pp. 22
Author(s):  
Vladimir Mondrus ◽  
Dmitrii Sizov
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Analytical Method ◽  
One Dimensional ◽  
Numerical Analytical Method ◽  
The Finite Difference Method ◽  
Dimensional Wave

The article contains a solution to the problem of wave propagation in a one-dimensional rod from the initial impact. A numerical-analytical method is used to solve the problem. The numerical part of the method is based on the application of the idea of the finite difference method. The analytical part uses the concept of Green’s function to solve the problem in terms of the spatial coordinate in the considered area. The results include graphs of the solution obtained at different points in time.

The role and application of entropy terms for acoustic wave modeling by the finite‐difference method

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1457-1465 ◽  
Author(s):  
M. A. Dablain
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Acoustic Wave Propagation ◽  
Central Difference ◽  
Central Difference Scheme ◽  
One Dimensional ◽  
The Finite Difference Method

The significance of entropy‐like terms is examined within the context of the finite‐difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central‐difference scheme, and (2) the Lax‐Wendroff two‐step scheme. Numerical results are presented comparing the short‐wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one‐dimensional source is used.

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