György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Introduction

Although a wide range of mathematical knowledge is included in the university curriculum, the practical use is often not immediately clear, or would be only made clear during later stages of studies. Furthermore, in engineering practice, there are many analytical solutions that can be very complicated, and the effort involved to follow them through might not be reflected in the final outcome, as the high level of accuracy or sophistication might not be required to solve a considerably simpler, practical problem at hand. Instead of looking for a „correct” mathematically perfectly accurate solution, many times we can settle with a solution that is although not 100% accurate but satisfies our goals and expectations. In these group of problems, we need to also include problems which can’t be reasonably defined in mathematical terms, but we can do very good approximation using numerical methods such as finite element, finite difference or finite volume methods. This is the philosophy behind the development and usage of the various numerical methods, and that is the topic of this set of lecture notes.

Numerical methods

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 283 4

This book on Numerical Methods is part of the Transportation and Vehicle Engineering Faculty’s curriculum at the Budapest University of Technology and Economics, created under the Stipendium Hungaricum Scholarship Programme. The book demonstrates the aim of developing and using numerical methods. Instead of relying on more complicated and expensive analytical solution methods, simpler arithmetical equations are used to approximate the accurate solution with the required level of accuracy. After discussing the various sources and propagation of solution errors, the book discusses the solution of single variable equations and system of equations. Following chapters describe the two main curve fitting methods; approximation and interpolation. These chapters are followed by the numerical differentiation and integration methods, then finally the numerical solutions for ordinary and partial differentiation equations are outlined. MATLAB is one of the most popular choice today for numerical computing, with its user friendly, yet powerful computing capability. It is practically an industry standard for prototyping and new developments, and there is great value for students to be introduced to solving problems with MATLAB. Many chapters in the notes show examples implemented in MATLAB, with actual working code available to use and practice.

Hivatkozás: https://mersz.hu/bicsak-numerical-methods//

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