György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Parabolic Partial Differential Equations

The parabolic partial differential equations can be solved mainly with two technics: the finite-difference (FD) method and Crank-Nicolson (CN) method. Their goal is similar as earlier: deriving a suitable difference equation that generates the solution estimations at mesh points. The main problem with parabolic PDEs, that the divergence (not converging to a solution) cannot be eliminated completely, not even by refining the grid size. To assure convergence, additional conditions have to be determined.

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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