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Microfluidics: Modeling, Mechanics and Mathematics by Bastian E. Rapp

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Chapter 25

Numerical Methods for Linear Systems of Equations

25.1 Introduction

Until now we have mostly restricted ourselves to finding analytical solutions to most of the equations. In many cases, we were only able to do so by applying certain simplifications. However, we often encountered equations that are simply unsolvable analytically. For these equations, we have to turn to numerical methods. In the following sections, we will study the most important techniques commonly encountered and discuss examples of these methods. Most of the methods can be implemented conveniently in any programming language and we will make heavy use of both Maple and C in this chapter. We will first start by discussing numerical methods for solving linear systems ...

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