"Dissipative structures" is a concept which has recently been used in physics to discuss the formation of structures organized in space and/or time at the expense of the energy flowing into the system from the outside. The space-time structural organization of biological systems starting from the subcellular level up to the level of ecological systems, coherent structures in laser and of elastic stability in mechanics, instability in hydro plasma physics, problems dynamics leading to the development of turbulence, behavior of electrical networks and chemical reactors form just a short list of problems treated in this framework. Mathematical models constructed to describe these systems are usually nonlinear, often formed by complicated systems of algebraic, ordinary differ ential, or partial differential equations and include a number of character istic parameters. In problems of theoretical interest as well as engineering practice, we are concerned with the dependence of solutions on parameters and particularly with the values of parameters where qualitatively new types of solutions, e.g., oscillatory solutions, new stationary states, and chaotic attractors, appear (bifurcate). Numerical techniques to determine both bifurcation points and the depen dence of steady-state and oscillatory solutions on parameters are developed and discussed in detail in this text. The text is intended to serve as a working manual not only for students and research workers who are interested in dissipative structures, but also for practicing engineers who deal with the problems of constructing models and solving complicated nonlinear systems.

A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.

This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

An annual volume presenting substantive survey articles in numerical analysis and scientific computing.