Stability and accuracy analysis of some fully-discrete algorithms for the one-dimensional second-order wave equation

1984 ◽  
Vol 19 (4) ◽  
pp. 665-668 ◽  
Author(s):  
Thomas J.R. Hughes ◽  
Tayfun E. Tezduyar
Keyword(s):  
Wave Equation ◽  
Second Order ◽  
Accuracy Analysis ◽  
One Dimensional ◽  
Fully Discrete ◽  
Discrete Algorithms ◽  
Second Order Wave Equation ◽  
The One ◽  
Stability And Accuracy

CTCS Schemes for Second Order Wave Equation: Numerical Results and Spectral Analysis

2021 ◽  
Vol 55 ◽  
pp. 47-65
Author(s):  
Appanah Rao Appadu ◽  
Gysbert Nicolaas de Waal
Keyword(s):  
Spectral Analysis ◽  
Wave Equation ◽  
Numerical Experiments ◽  
Finite Difference Methods ◽  
Second Order ◽  
Numerical Results ◽  
Order Accuracy ◽  
Constant Coefficients ◽  
Second Order Wave Equation ◽  
The One

IIn this paper, two finite difference methods are used to solve the one-dimensional second order wave equation with constant coefficients subject to specified initial and boundary conditions. Two numerical experiments are considered. The two methods are Central in Time and Central in Space scheme with second order accuracy in both time and space, abbreviated as CTCS (2,2) and Central in Time and Central in Space scheme with second order accuracy in time and fourth order accuracy in space, abbreviated as CTCS (2,4). Properties such as consistency and stability are studied. We also perform spectral analysis of dispersive and dissipative properties of the two methods. Two numerical experiments are considered, and the numerical results are displayed.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave
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