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Stability of Numerical Methods for Solving Second-Order Hyperbolic Equations with a Small Parameter
- Source :
- Doklady Mathematics. 101:30-35
- Publication Year :
- 2020
- Publisher :
- Pleiades Publishing Ltd, 2020.
-
Abstract
- We study a symmetric three-level (in time) method with a weight and a symmetric vector two-level method for solving the initial-boundary value problem for a second-order hyperbolic equation with a small parameter $$\tau > 0$$ multiplying the highest time derivative, where the hyperbolic equation is a perturbation of the corresponding parabolic equation. It is proved that the solutions are uniformly stable in $$\tau $$ and time in two norms with respect to the initial data and the right-hand side of the equation. Additionally, the case where $$\tau $$ also multiplies the elliptic part of the equation is covered. The spacial discretization can be performed using the finite-difference or finite element method.
- Subjects :
- Discretization
Uniformly stable
General Mathematics
Numerical analysis
010102 general mathematics
Mathematical analysis
Perturbation (astronomy)
01 natural sciences
Finite element method
010305 fluids & plasmas
0103 physical sciences
Time derivative
0101 mathematics
Hyperbolic partial differential equation
Mathematics
Subjects
Details
- ISSN :
- 15318362 and 10645624
- Volume :
- 101
- Database :
- OpenAIRE
- Journal :
- Doklady Mathematics
- Accession number :
- edsair.doi...........e04f69cde6038a2f7baf69e45597a13c