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undergraduate thesis
Numeričko rješavanje Laplaceove jednadžbe
Split: University of Split, University of Split, Faculty of science, 2020. urn:nbn:hr:166:764911
Matković, Mijo
University of Split
Faculty of Science
Department of Physics

Institutional repository: Repository of Faculty of Science

Cite this document

Matković, M. (2020). Numeričko rješavanje Laplaceove jednadžbe (Undergraduate thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:764911

Matković, Mijo. "Numeričko rješavanje Laplaceove jednadžbe." Undergraduate thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:764911

Matković, Mijo. "Numeričko rješavanje Laplaceove jednadžbe." Undergraduate thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:764911

Matković, M. (2020). 'Numeričko rješavanje Laplaceove jednadžbe', Undergraduate thesis, University of Split, Faculty of Science, accessed 20 December 2024, https://urn.nsk.hr/urn:nbn:hr:166:764911

Matković M. Numeričko rješavanje Laplaceove jednadžbe [Undergraduate thesis]. Split: University of Split, Faculty of Science; 2020 [cited 2024 December 20] Available at: https://urn.nsk.hr/urn:nbn:hr:166:764911

M. Matković, "Numeričko rješavanje Laplaceove jednadžbe", Undergraduate thesis, University of Split, Faculty of Science, Split, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:166:764911

Metadata
TitleNumeričko rješavanje Laplaceove jednadžbe
Title (english)Numerical solution of Laplace´s equation
AuthorMijo Matković
MentorPetar Stipanović (mentor)
Committee memberPetar Stipanović (predsjednik povjerenstva)
Committee memberLarisa Zoranić (član povjerenstva)
Committee memberViktor Cikojević (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Physics)
Split
Defense date and country2020-09-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Laplaceova jednadžba jedna je od osnovnih jednadžbi elektrodinamike. Ona opisuje izgled električnog potencijala u točkama prostora gdje ne postoji nikakav naboj. Sama jednadžba je homogena parcijalna diferencijalna jednadžba drugog reda. U slučajevima kada su rubni uvjeti netrivijalni ova jednadžba je zahtjevna za analitičko rješavanje, te se primjenjuju numeričke metode. U ovom završnom radu provodi se validacija numeričkih metoda pri rješavanju Laplaceove jednadžbe. Ispravnost koda je provjerena na 2 jednostavna primjera, te je uočena velika sličnost s poznatim analitičkim rješenjem (postignuta su vrlo mala odstupanja). Nakon što je provjerena ispravnost koda, u mogućnosti smo numerički riješiti Laplaceovu jednadžbu za netrivijalne rubne uvjete (često nerješive analitički), odnosno primijeniti izrađeni programski kod za bilo kakve rubne uvjete u dvodimenzionalnom (2D) prostoru.
Abstract (english)
Laplace’s equation is one of the fundemental equations of electrodynamics. It describes the behaviour of electric potential in the area without charge. Laplace’s equation is homogenous partial differential equation of second order. It is often (when boundary conditions are non-trivial) difficult to solve analytically, so numerical methods of solving are necessary. In this thesis validation of numerical methods for solving Laplace’s equation is performed. Validity of the code was checked on 2 simple examples, and great level of similarity with known analytical solution was detected (very small deviations were observed). After validating our code, we are able to solve Laplace’s equation for non-trivial boundary conditions (often unsolvable analitycally), that is, apply our program code to any boundary conditions in two-dimensional (2D) space.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:764911
Study programmeTitle: Physics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) fizike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) fizike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
Terms of useLicence In copyright icon
Created on2021-01-19 11:34:18