scholarly journals Fourth-order energy-preserving locally implicit time discretization for linear wave equations

2015 ◽  
Vol 106 (8) ◽  
pp. 593-622 ◽  
Author(s):  
J. Chabassier ◽  
S. Imperiale
Keyword(s):  
Fourth Order ◽  
Wave Equations ◽  
Time Discretization ◽  
Implicit Time ◽  
Linear Wave ◽  
Order Energy ◽  
Linear Wave Equations

scholarly journals Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations

2020 ◽  
Vol 54 (3) ◽  
pp. 845-878
Author(s):  
Juliette Chabassier ◽  
Julien Diaz ◽  
Sébastien Imperiale
Keyword(s):  
Convergence Analysis ◽  
Fourth Order ◽  
Wave Equations ◽  
Energy Analysis ◽  
Linear Wave ◽  
Convergence Properties ◽  
Order Energy ◽  
Linear Wave Equations ◽  
The Stability ◽  
Modified Equation

This paper deals with the construction of a family of fourth order, energy consistent, explicit time discretizations for dissipative linear wave equations. The schemes are obtained by replacing the inversion of a matrix, that comes naturally after using the technique of the Modified Equation on the second order Leap Frog scheme applied to dissipative linear wave equations, by explicit approximations of its inverse. The stability of the schemes are studied using an energy analysis and a convergence analysis is carried out. Numerical results in 1D illustrate the space/time convergence properties of the schemes and their efficiency is compared to more classical time discretizations.

scholarly journals On inverse problem for a class of fourth order strongly damped wave equations

2018 ◽  
Vol 20 ◽  
pp. 02006
Author(s):  
Nam Danh Hua Quoc ◽  
Can Nguyen Huu ◽  
Au Vo Van ◽  
Binh Tran Thanh
Keyword(s):  
Inverse Problem ◽  
Fourth Order ◽  
Wave Equations ◽  
A Priori ◽  
Linear Wave ◽  
Ill Posed ◽  
Convergence Estimates ◽  
Linear Wave Equations ◽  
In The Beginning ◽  
Strongly Damped

In this paper, we study the initial inverse problem for a class of fourth order strongly damped linear wave equations. In the beginning, we show that the problem is ill-posed in the sense of Hadamard. Next, we propose the method called: the Fourier truncation method for stabilizing the problem. Convergence estimates are established under a priori regularity assumptions on the problem data.

Uniqueness for stochastic non-linear wave equations

2007 ◽  
Vol 67 (12) ◽  
pp. 3287-3310 ◽  
Author(s):  
Martin Ondreját
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations
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