Periodic Integral and Pseudodifferential Equations with Numerical Approximation

Kirjan Periodic Integral and Pseudodifferential Equations with Numerical Approximation (2001) on kirjoittanut Jukka Saranen. Kirjan kieli on englanti, ja sen on kustantanut Springer-Verlag Berlin and Heidelberg GmbH Co. K. Kirja on laajuudeltaan 452 sivua ja se on sidottu.

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.