
Periodic Integral and Pseudodifferential Equations with Numerical Approximation
Springer (Publisher)
Published on 6. November 2001
Book
Hardback
XI, 452 pages
978-3-540-41878-8 (ISBN)
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.
More details
Series
Edition
2002 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XI, 452 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 30 mm
Weight
863 gr
ISBN-13
978-3-540-41878-8 (9783540418788)
DOI
10.1007/978-3-662-04796-5
Schweitzer Classification
Other editions
Additional editions

Jukka Saranen | Gennadi Vainikko
Periodic Integral and Pseudodifferential Equations with Numerical Approximation
Book
12/2010
Springer
€106.99
Shipment within 7-9 days
Content
1 Preliminaries.- 2 Single Layer and Double Layer Potentials.- 3 Solution of Boundary Value Problems by Integral Equations.- 4 Singular Integral Equations.- 5 Boundary Integral Operators in Periodic Sobolev Spaces.- 6 Periodic Integral Equations.- 7 Periodic Pseudodifferential Operators.- 8 Trigonometric Interpolation.- 9 Galerkin Method and Fast Solvers.- 10 Trigonometric Collocation.- 11 Integral Equations on an Open Arc.- 12 Quadrature Methods.- 13 Spline Approximation Methods.