Numerical Calculation Methods
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Electric Fields in Composite Dielectrics and their Applications
Author: Tadasu Takuma
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-08-05
An accurate quantitative picture of electric field distribution is essential in many electrical and electronic applications. In composite dielectric configurations composed of multiple dielectrics, anomalous or unexpected behavior of electric fields may appear when a solid dielectric is in contact with a conductor or another solid dielectric. The electric field near the contact point may become higher than the original field not only in the surrounding medium but also in the solid dielectric. Theoretically it may become infinitely high, depending on the contact angle. Although these characteristics are very important in a variety of applications, they have been clarified only recently using analytical and numerical calculation methods, and this is the first book to cover these new findings. Electric Fields in Composite Dielectrics and Their Applications describes the fundamental characteristics and practical applications of electric fields in composite dielectrics. The focus is on the field distribution (and the resultant force when appropriate) near points of contact. Applications include insulation design of high-voltage equipment with solid insulating supports, utilization of electrostatic force on dielectric particles in electrophotography and electrorheological fluids, and others. Electric Fields in Composite Dielectrics and Their Applications also explains the calculation methods used to analyze electric fields in composite dielectrics.
Numerical Methods using MATLAB
Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied. Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical. Numerical Methods with MATLAB presents each topic in a concise and readable format to help you learn fast and effectively. It is not intended to be a reference work to the conceptual theory that underpins the numerical methods themselves. A wide range of reference works are readily available to supply this information. If, however, you want assistance in applying numerical methods then this is the book for you.
Introduction to Numerical Methods in Differential Equations
Author: Mark H. Holmes
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-04-05
The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let’s start with the expression “di?erential equations.” These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: “numerical methods.” This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.