Periodic Integral and Pseudodifferential Equations with Numerical Approximation
By: by Jukka Saranen, Gennadi Vainikko
Contributors: Vainikko, Gennadi
Series: Springer Monographs in Mathematics; Springer Monographs in Mathematics
Publisher: Springer Berlin Heidelberg
Published: 2002
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 452
ISBN-13: 9783642075384; 9783662047965
Subjects: Mathematics; Global analysis (Mathematics); Computer science
Description: 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.
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