Periodic Integral and Pseudodifferential Equations with Numerical Approximation

✍ Scribed by Jukka Saranen, Gennadi Vainikko (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2002
• Tongue: English
• Leaves: 460
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Preliminaries....Pages 1-34
Single Layer and Double Layer Potentials....Pages 35-70
Solution of Boundary Value Problems by Integral Equations....Pages 71-103
Singular Integral Equations....Pages 105-132
Boundary Integral Operators in Periodic Sobolev Spaces....Pages 133-165
Periodic Integral Equations....Pages 167-198
Periodic Pseudodifferential Operators....Pages 199-238
Trigonometric Interpolation....Pages 239-254
Galerkin Method and Fast Solvers....Pages 255-291
Trigonometric Collocation....Pages 293-324
Integral Equations on an Open Arc....Pages 325-354
Quadrature Methods....Pages 355-400
Spline Approximation Methods....Pages 401-440
Back Matter....Pages 441-452

✦ Subjects

Analysis; Computational Mathematics and Numerical Analysis