Fundamental Numerical Methods for Electrical Engineering

The book presents fundamental numerical methods which are most frequently applied in the electrical (electronic) engineering. A scope of this book is rather wide and includes solving the sets of linear and nonlinear equations, interpolation and approximation of the functions of one variable, integration and differentation of the functions of one and two variables, integration of the ordinary differential equations, and integration the partial differential equations of two variables. All methods discussed are illustrated with real-world examples of applications. It is shown how real engineering questions can be transformed into the corresponding mathematical problems and next effectively solved by using appropriate numerical methods. Usually, for teaching reasons, mathematical problems are solved step by step, and illustrated by neumerous intermediate results. Thus, it is not only explained how the problem can be solved, but the details of the solution are also demonstrated. In Chapter 7 for instance three electrical rectifying devices and a transmission-line non- homogeneous impedance transformer are analyzed in this manner. Similarly, in Chapter 8 different aspects of Laplace boundary value problem formulated for various kinds of single and coupled TEM transmission lines are presented. In other words, six standard TEM transmission lines are investigated by means of the finite difference method. It is shown how a partial differential equation of the second order can be approximated by the corresponding difference equation defined on interior and boundary nodes of the introduced grid. At the next stage, the set of linear equations, formulated in this way, is recurrently solved by using the effective SOR technique. Additionally, ideas of " fictitious nodes " and the " even and odd mode excitations " methods are explained and illustrated. All methods and computational results, presented in the book, are of significant practical value. Thus, this book may be especially helpful for students of electronic departments of technical universities and for practicing engineers.

Résumé
Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: computer-aided design (CAD) computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, elaboration of the initial, possibly general electric structure, determination of mathematical model of the system on the basis of the adopted electric structure, determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, preparation of design and technological documentation, manufacturing of model (prototype) series, according to the prepared docum- tation, testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.

Contenu
Methods for Numerical Solution of Linear Equations.- Methods for Numerical Solving the Single Nonlinear Equations.- Methods for Numerical Solution of Nonlinear Equations.- Methods for the Interpolation and Approximation of One Variable Function.- Methods for Numerical Integration of One and Two Variable Functions.- Numerical Differentiation of One and Two Variable Functions.- Methods for Numerical Integration of Ordinary Differential Equations.- The Finite Difference Method Adopted for Solving Laplace Boundary Value Problems.