Periodic Integral and Pseudodifferential Equations with Numerical Approximation

Gennadi Vainikko

ISBN 10: 3540418784 / ISBN 13: 9783540418788

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2001, 2001

Riguardo questo articolo

Neuware -Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 468 pp. Englisch. Codice articolo 9783540418788

Dati bibliografici

Titolo: Periodic Integral and Pseudodifferential ...

Casa editrice: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2001

Data di pubblicazione: 2001

Legatura: Buch

Condizione: Neu

Descrizione articolo

Riassunto:

An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Dalla quarta di copertina:

Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.