Error study on numerical approximation of radiation boundary condition for one-dimensional wave equation

1993 ◽  
Vol 9 (6) ◽  
pp. 475-482 ◽  
Author(s):  
L. Zhu ◽  
C. W. Li
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Numerical Approximation ◽  
Radiation Boundary Condition ◽  
One Dimensional ◽  
Radiation Boundary ◽  
Dimensional Wave ◽  
Error Study

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

Complete Radiation Boundary Conditions for Convective Waves

2012 ◽  
Vol 11 (2) ◽  
pp. 610-628 ◽  
Author(s):  
Thomas Hagstrom ◽  
Eliane Bécache ◽  
Dan Givoli ◽  
Kurt Stein
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Radiation Boundary Condition ◽  
Linearized Euler Equations ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Optimal Efficiency ◽  
Radiation Boundary ◽  
Scalar Equations

AbstractLocal approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4].

scholarly journals The classical solution of one problem of an absolutely inelastic impact on a long elastic semi-infinite bar

2021 ◽  
Vol 57 (4) ◽  
pp. 417-427
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Classical Solution ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Bottom Boundary ◽  
One Dimensional ◽  
Inelastic Impact ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom boundary, the Cauchy conditions are specified, meanwhile, the second of them has a discontinuity of the first kind at one point. The smooth boundary condition, which has the first and the second order derivatives, is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved and the conditions are established under which a piecewise-smooth solution exists. The problem with matcing conditions is considered.

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