Stable computations by discrete mollification
The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main result...
- Autores:
-
Acosta, Carlos Daniel
Mejía, Carlos Enrique
- Tipo de recurso:
- Book
- Fecha de publicación:
- 2004
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/78135
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/78135
- Palabra clave:
- 510 - Matemáticas
Ecuaciones diferenciales hiperbólicas
Soluciones numéricas
Diferencias finitas
Leyes de conservación
Matemáticas
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
| Summary: | The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main results and recent developments in discrete mollification and discusses several important topics of current research interest. The book develops and applies numerical methods based on discrete mollification for a variety of situations arising in applied mathematics, including convection-diffusion equations, conservation laws, strongly degenerate parabolic equations and several system identification problems. For each topic there are theoretical considerations concerning stability and convergence and a generous amount of illustrative examples. The intended audience for this book includes mathematicians, physicists and engineers. |
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