Numerical Analysis: Proceedings of the 8th Biennial Conference Held at Dundee, Scotland, June 26-29, 1979 (Lecture notes in mathematics ; v. 773)

Proceedings of the 8th Biennial Conference Held at Dundee, 1979 "Classical Circuit Theory provides readers with the fundamental, analytic properties of linear circuits that are important to the design of conventional and non-conventional circuits in modern communication systems. These properties include the relations between phase and gain, between the real and imaginary parts, and between phase and group delay. They also include the fundamental limitations on gain and bandwidth, which are important in broadband matching in amplifier design. The idea that an impedance function is a positive real function and that a transfer function is bounded-real, forms the basis for analytic design of all conventional filters. At the same time, mathematical programming tools are now widely available so that design of non-conventional circuits by optimization is but a few mouse clicks away." "Every new concept within the material is illustrated with one or more examples. There are exercises and problems at the end of the chapters. Some may be suitable for term projects. The design techniques presented are also illustrated step by step with easy-to-follow examples."--Jacket A generalized conjugate direction method and its application on a singular perturbation problem....Pages 1-11 Some implementation schemes for implicit Runge-Kutta methods....Pages 12-24 Best approximation in tensor product spaces....Pages 25-32 Monotonicity and free boundary value problems....Pages 33-45 Computing eigenvectors (and eigenvalues) of large, symmetric matrices using Lanczos tridiagonalization....Pages 46-63 Horizontal line analysis of the multidimensional porous medium equation: Existence, rate of convergence and maximum principles....Pages 64-82 Numerical methods for phase-plane problems in ordinary differential equations....Pages 83-97 On the use of exact penalty functions to determine step length in optimization algorithms....Pages 98-109 Petrov-Galerkin methods for non-self-adjoint problems....Pages 110-118 Collocation and perturbed collocation methods....Pages 119-132 Modular analysis of numerical software....Pages 133-145 The numerical solution of turbulent flow problems in general geometry....Pages 146-163 The rate of convergence of a multiple grid method....Pages 164-184 Classical circuit theory is a mathematical theory of linear, passive circuits, namely, circuits composed of resistors, capacitors and inductors. Like many a thing classical, it is old and enduring, structured and precise, simple and elegant. It is simple in that everything in it can be deduced from ?rst principles based on a few physical laws. It is enduring in that the things we can say about linear, passive circuits are universally true, unchanging. No matter how complex a circuit may be, as long as it consists of these three kinds of elements, its behavior must be as prescribed by the theory. The theory tells us what circuits can and cannot do. As expected of any good theory, classical circuit theory is also useful. Its ulti mate application is circuit design. The theory leads us to a design methodology that is systematic and precise. It is based on just two fundamental theorems: that the impedance function of a linear, passive circuit is a positive real function, and that the transfer function is a bounded real function, of a complex variable.