- Email: [email protected]
Elements of Differentiable Dynamics and Bifurcation Theory
Book Reviews Computational Methods for Process Simulation W. Fred Ramirez Butterworths, London, UK 1989, $52.95 This book deals with the solution of process simulation by means of numerical methods and makes use of software that is available in the IMSL library. The book consists of eight chapters that cover the following subjects: macroscopic balances for lumped parameter systems, steady-state simulation of lumped systems, dynamic simulation of lumped parameter systems, dynamics of reaction kinetics systems, vapor-liquid equilibrium systems, microscopic balances for distributed parameter systems, solution of boundary value problems, and finite difference methods for partial differential equations. Each chapter is well illustrated with examples, figures, exercises for the reader, computer programs, flow diagrams, and bibliography. The book also contains two appendices; Appendix A summarizes some analytical solutions of firstand second-order ordinary differential equations, and Appendix B lists the IMSL subroutines used in the book. Chapter 1 deals with standard material on the development ofthe equations governing the macroscopic principles of conservation of mass, linear momentum, and energy. It also provides a “method of working problems” and “information-flow diagrams,” which are used repeatedly throughout the text. Chapter 2 briefly describes solution methods for systems of linear and nonlinear algebraic equations and the functionality matrix developed by Book and Ramirez in 1984. In particular, Chapter
2 includes the methods of Gauss elimination, bisection, regula falsi, and Newton. Chapter 3 describes the methods of Euler and Runge-Kutta and multisteps for the solution of first-order ordinary differential equations. Also included in Chapter 3 is a brief description of Gear’s method for the solution of stiff ordinary differential equations. Applications of the methods presented in Chapter 3 are also presented in Chapter 4, which deals with the numerical simulation of reaction kinetics systems, and in Chapter 5, which deals with vaporliquid equilibrium systems. Chapter 6 presents standard material on the equations governing the microscopic principles of conservation of mass, linear momentum, and energy. Chapter 6 lists the partial differential equations of mass, linear momentum, and energy in tabular form and presents examples dealing with stagnant films, pipe flow, heat conduction in composite walls, and tubular reactors; some of these examples have been previously solved and published by the book’s author. Chapter 7 describes shooting techniques, superposition methods for linear boundary value problems, quasi-linearization, and the method of adjoints. Chapter 8 describes explicit and implicit numerical methods, the state-variable formulation, orthogonal collocation, and the method of weighted residuals, which are applied to a variety of problems. It is somewhat surprising that the author does not mention the famous “cell-Reynolds number” problem when dealing with convection. The book clearly illustrates the important role that numerical methods have played in process simulation and chemical engineering and may be used in chemical engineering courses at the un-
dergraduate level to expose the students to numerical techniques. J. I. Ramos
Elements of Differentiable Dynamics and Bifurcation Theory David Rue/e Academic Press, inc., New York, 1989, 187 pp., $27.50 This book is an introduction to hyperbolicity and bifurcation theory that emphasizes ideas rather than proofs. The book consists of three parts. Part 1 deals with differentiable dynamical systems, manifolds, fixed points, periodic orbits, attractors, and bifurcations. Part 1 is well illustrated with numerous figures, footnotes, and exercises. Part 2 deals with bifurcation theory, local analysis, dissipative systems, and hyperbolic invariant sets. The third part of the book consists of four appendices on set theory, topology, topological dynamics, ergodic theory, and axiom A. The book has a good list of references in which the proofs that are omitted in the text can be found; the list of references also includes papers dealing with chaos. The book is very well written, contains very few typographical errors, and would be useful to mathematicians or mathematically inclined students for its clear exposition of the ideas regarding differentiable dynamical systems and bifurcation theory. It is a very welcome addition to the literature on nonlinear dynamics.
Appl. Math. Modelling,
J. 1. Ramos
1990, Vol. 14, August
445
2 includes the methods of Gauss elimination, bisection, regula falsi, and Newton. Chapter 3 describes the methods of Euler and Runge-Kutta and multisteps for the solution of first-order ordinary differential equations. Also included in Chapter 3 is a brief description of Gear’s method for the solution of stiff ordinary differential equations. Applications of the methods presented in Chapter 3 are also presented in Chapter 4, which deals with the numerical simulation of reaction kinetics systems, and in Chapter 5, which deals with vaporliquid equilibrium systems. Chapter 6 presents standard material on the equations governing the microscopic principles of conservation of mass, linear momentum, and energy. Chapter 6 lists the partial differential equations of mass, linear momentum, and energy in tabular form and presents examples dealing with stagnant films, pipe flow, heat conduction in composite walls, and tubular reactors; some of these examples have been previously solved and published by the book’s author. Chapter 7 describes shooting techniques, superposition methods for linear boundary value problems, quasi-linearization, and the method of adjoints. Chapter 8 describes explicit and implicit numerical methods, the state-variable formulation, orthogonal collocation, and the method of weighted residuals, which are applied to a variety of problems. It is somewhat surprising that the author does not mention the famous “cell-Reynolds number” problem when dealing with convection. The book clearly illustrates the important role that numerical methods have played in process simulation and chemical engineering and may be used in chemical engineering courses at the un-
dergraduate level to expose the students to numerical techniques. J. I. Ramos
Elements of Differentiable Dynamics and Bifurcation Theory David Rue/e Academic Press, inc., New York, 1989, 187 pp., $27.50 This book is an introduction to hyperbolicity and bifurcation theory that emphasizes ideas rather than proofs. The book consists of three parts. Part 1 deals with differentiable dynamical systems, manifolds, fixed points, periodic orbits, attractors, and bifurcations. Part 1 is well illustrated with numerous figures, footnotes, and exercises. Part 2 deals with bifurcation theory, local analysis, dissipative systems, and hyperbolic invariant sets. The third part of the book consists of four appendices on set theory, topology, topological dynamics, ergodic theory, and axiom A. The book has a good list of references in which the proofs that are omitted in the text can be found; the list of references also includes papers dealing with chaos. The book is very well written, contains very few typographical errors, and would be useful to mathematicians or mathematically inclined students for its clear exposition of the ideas regarding differentiable dynamical systems and bifurcation theory. It is a very welcome addition to the literature on nonlinear dynamics.
Appl. Math. Modelling,
J. 1. Ramos
1990, Vol. 14, August
445