György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Partial Differential Equations generally

In the case of PDEs the equation involves a dependent-variable function with at least two independent variables and the function’s partial derivatives. The highest order of the derivative determines the order of the PDE, marked with n. We make difference between linear PDEs (the dependent variable’s and its derivatives’ highest order is first degree) or nonlinear. If the PDE includes the dependent variable and its derivatives only, then we are dealing with a homogenous PDE. Of course, if there are other terms, it is a non-homogenous PDE.

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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