Numerical Solutions of PDEs Involving Interfaces and Irregular Domains
Interface problems arise when there are two different materials, such as water and oil, or the same material at different states, such as water and ice. If partial or ordinary differential equations are used to model these applications, the parameters in the governing equations are typically discontinuous across the interface separating the two ......
The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications ......
When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic ......
First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge elgenvalue problems. It deals with "symmetric" problems. However, in this book, "symmetric" also encompasses numerical procedures for computing singular values and vectors of real ......
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and ......
This text provides an in-depth analysis of the mathematical foundations of the finite element method. It is a comprehensive reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis. It includes many useful figures and exercises of ......
This second edition of the popular "A Multigrid Tutorial" preserves the introductory spirit of the first edition, while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear ......
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential ......
In this follow-up to Afternotes on Numerical Analysis (SIAM, 1996) the author continues to bring the immediacy of the classroom to the printed page. Like the original undergraduate volume, Afternotes goes to Graduate School is the result of the author writing down his notes immediately after giving each lecture; in this case the afternotes are the ......
