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dc.contributor.advisorAbou Salem, Walid K.en_US
dc.contributor.advisorSzmigielski, Jaceken_US
dc.creatorRostamiforooshani, Mehdien_US
dc.date.accessioned2013-08-30T12:00:10Z
dc.date.available2013-08-30T12:00:10Z
dc.date.created2013-08en_US
dc.date.issued2013-08-29en_US
dc.date.submittedAugust 2013en_US
dc.identifier.urihttp://hdl.handle.net/10388/ETD-2013-08-1152en_US
dc.description.abstractRenormalization Group (RG) method is a general method whose aim is to globally approximate solutions to differential equations involving a small parameter. In this thesis, we will give an algorithm for the RG method to generate the RG equation needed in the process of finding an approximate solution for ODEs. In chapter 1, we have some introduction to perturbation theory and introducing some traditional methods in perturbation theory. In chapter 2 we compare the results of RG and other conventional methods using numerical or explicit methods. Thereafter, in chapter 3, we rigorously compare the approximate solution obtained using the RG method and the true solution using two classes of system of ordinary differential equations. In chapter 4, we present a simplified RG method and apply it to the second order RG. In chapter 5 we briefly explain the first order Normal Form (NF) theory and then its relation to the RG method. Also a similar geometric interpretation for the RG equation and NF's outcome has been provided. In the Appendix, we have added definitions and proofs used in this thesis. The RG method is much more straightforward than other traditional methods and does not require prior information about the solutions. One begins with a naive perturbative expansion which already contains all the necessary information that we need to construct a solution. Using RG, there is no need to asymptotically match the solutions in the overlapping regions, which is a key point in some other methods. In addition, the RG method is applicable to most of perturbed differential equations and will produce a closed form solution which is, most of the times, as accurate as or even more accurate than the solutions obtained by other conventional methods.en_US
dc.language.isoengen_US
dc.subjectKeyword1: Perturbation Theory, Keyword2: Traditional Methods, Keyword3: Perturbed Differential Equations.en_US
dc.titleRenormalization Group Methoden_US
thesis.degree.departmentMathematics and Statisticsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Science (M.Sc.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US
dc.contributor.committeeMemberBickis, Miken_US
dc.contributor.committeeMemberShevyakov, Alexeyen_US


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