György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Numerical Solution of Differential Equations – Initial Value Problems

When solving ordinary differential equations (ODE) numerically, the most common is to take a bottom-up approach. This would involve evaluating the highest order of differential, and step by step working back to the final level of equations for each value of the independent variable (most commonly time). Once one state of the system is solved by this approach, all the other states can be calculated by varying the independent variable and implementing a time-marching solution. Note that it is referred to as time marching, although the independent variable might not be actually defined as time.

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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