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Symmetry methods and some nonlinear differential equations: Background and illustrative examples
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Symmetrimetoder och några icke-linjära differentialekvationer : Bakgrund och illustrativa exempel (Swedish)
Abstract [en]

Differential equations, in particular the nonlinear ones, are commonly used in formulating most of the fundamental laws of nature as well as many technological problems, among others. This makes the need for methods in finding closed form solutions to such equations all-important. In this thesis we study Lie symmetry methods for some nonlinear ordinary differential equations (ODE). The study focuses on identifying and using the underlying symmetries of the given first order nonlinear ordinary differential equation. An extension of the method to higher order ODE is also discussed. Several illustrative examples are presented.

Abstract [sv]

Differentialekvationer, framförallt icke-linjära, används ofta vid formulering av fundamentala naturlagar liksom många tekniska problem. Därmed finns det ett stort behov av metoder där det går att hitta lösningar i sluten form till sådana ekvationer. I det här arbetet studerar vi Lie symmetrimetoder för några icke-linjära ordinära differentialekvationer (ODE). Studien fokuserar på att identifiera och använda de underliggande symmetrierna av den givna första ordningens icke-linjära ordinära differentialekvationen. En utvidgning av metoden till högre ordningens ODE diskuteras också. Ett flertal illustrativa exempel presenteras.

Place, publisher, year, edition, pages
2017. , p. 41
Keywords [en]
Lie symmetries, nonlinear ordinary differential equations, reduction of order, invariant solutions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-48020OAI: oai:DiVA.org:kau-48020DiVA, id: diva2:1078213
Subject / course
Mathematics
Educational program
Mathematics Programme (180 ECTS credits)
Supervisors
Examiners
Available from: 2017-03-03 Created: 2017-03-02 Last updated: 2018-11-20Bibliographically approved

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