• Global artificial boundary conditions of second order elliptic differential equations.- Global artificial boundary conditions of Navie Equations and Stokes Equations.- Global artificial boundary conditions of heat equation and Schrodinger Equation.- Fully absorbing boundary conditions of wave equations, Klein-Gordan Equation and linear KdV Equation.- Discrete artificial boundary conditions.- Local artificial boundary conditions.- Implicit artificial boundary conditions.- Nonlinear artificial boundary conditions.- Applications.

"The book under review is focused on this broad approach, and is a comprehensive guide to such artificial boundary conditions for many PDEs of interest. ... The treatment is comprehensive as well as accessible, and the book is therefore invaluable both as a reference text and as the basis for a graduate course. ... The book under review is a substantial and well-written contribution to the area, and will be a valuable resource for both researchers and students." (Nilima Nigam, Mathematical Reviews, June, 2015) "It is an important contribution, and its assembly in book form is beneficial to those who would like to study the subject. ... The text is clear and easy to read. The book's format is pleasant to the eye and inviting. ... this book is a useful assembly of the authors' work on exact ABCs and related topics, which provides the reader with a collection of mathematical tools for the design and analysis of such ABCs." (Dan Givoli, SIAM Review, Vol. 56 (4), December, 2014)