This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs.

Methods for Solving Systems of Nonlinear Equations (CBMS-NSF Regional Conference Series in Applied Mathematics)

Science & Math

Rheinboldt, Werner C.

Mathematics

Society for Industrial & Applied

Dedicated to Professor Z. W. Birnbaum. Reliability and Fault Tree Analysis. Theoretical and Applied Aspects of System Reliability and Safety Assessment

Barlow, Richard E.

Nuclear Systems Reliability Engineering and Risk Assessment (Proceedings Series)

Fussell, J. B.

Numerical Solutions of Nonlinear Problems (Studies in Numerical Analysis 2)

Conference held by the Office of Naval Research, June 1984 Papers fall roughly into seven groups: one-dimensional transient problems, inverse problems in the frequency domain, multiparameter estimates for layered media, inverse problems as optimization problems, algorithms based on linearization and/or high-frequency asymptotics, numerical solution of boundary value problems, and modeling issues.

Inverse Problems of Acoustic and Elastic Waves

Pao, Yih-Hsing

Symes, William W.

Numerical Optimization 1984

334p burgundy hardback, fresh copy, from a college library, printed from typescript, graphs and diagrams,

Sparse Matrix Proceedings 1978

Society for Industrial and Applied Mathematics

Stewart, G. W.

Symposium on Sparse Matrix Computations (1978 Knoxville, Tenn.)

Electric Power Problems: The Mathematical Challenge

Politics & Social Sciences

Erisman, A. M.

Social Sciences

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. 
A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. 
Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods. 
Chapters 1 and 2 of the book describe in detail the theory of the inverse scattering transform. Chapter 3 discusses alternate methods for these exactly solvable problems and the interconnections among them. Physical applications are described in Chapter 4, where, for example, similarities between deep water waves and nonlinear optics become evident. Because of the fundamental role of linear theory, there is an extensive appendix that addresses the linear problems and their solutions.

Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Mathematics, No. 4)

Ablowitz, Mark J.

Segur, Harvey

Fourier Analysis of Numerical Approximations of Hyperbolic Equations

Vichnevetsky, Robert

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