A convergent finite difference scheme for the Ostrovsky-Hunter equation with Dirichlet boundary conditions (Q2273200)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A convergent finite difference scheme for the Ostrovsky-Hunter equation with Dirichlet boundary conditions |
scientific article |
Statements
A convergent finite difference scheme for the Ostrovsky-Hunter equation with Dirichlet boundary conditions (English)
0 references
18 September 2019
0 references
The authors study a generalization of the Ostrovsky-Hunter equation on a bounded domain with non-homogeneous Dirichlet boundary conditions. A finite difference scheme is proposed and is shown to converge to the unique entropy solution. The existence of entropy solutions for the initial-boundary value problem for the general Ostrovsky-Hunter equation is also demonstrated. Uniqueness is shown by employing Kružkov's doubling of variables technique. Several numerical examples are presented as illustration to the main results.
0 references
Ostrovsky-Hunter equation
0 references
short-pulse equation
0 references
Vakhnenko equation
0 references
finite difference methods
0 references
monotone scheme
0 references
existence
0 references
uniqueness
0 references
stability
0 references
convergence
0 references
entropy solution
0 references
Dirichlet boundary conditions
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
