Burgers denkleminin çözümü için bir yarı-analitik uygulama

Abstract

ÖZETYüksek Lisans Tezi%85*(56'(1./(0ø1ø1dg=h0hødø1%ø5<$5,-$1$/ø7ø.8<*8/$0$Derya TÜRKøQQÂhQLYHUVLWHVLFen Bilimleri Enstitüsü0DWHPDWLN$QDELOLP'DOÃ75 + x sayfa2005Tez'DQÃúPDQÃ'Ro'U$OLg='(ùBu tez yediEOÂPGHQROXúPDNWDGÃU%LULQFL EOÂPGH EX oDOÃúPDGD PRGHO SUREOHP RODUDN NXOODQÃODQ %XUJHUVGHQNOHPLKDNNÃQGDELOJLYHULOPHNWHGLUøNLQFLEOÂPGHNRQX/ODLOJLOLWHPHOWDQÃPODUWHRUHPOHUYH/QWHPOHUNÃVDFDWDQÃWÃOPDNWDGÃUÜçüncü bölümde, 0HWKRI RI /LQHV /QWHPL DoÃNODQDUDN ELU X/JXODPDVÃ/DSÃOPÃúWÃUDördüncü bölümde, Burgers denkleminin analitik çözümü verilmektedir.burada, OLQHHUOHúWLULOPLú%HúLQFL EOÂP EX oDOÃúPDQÃQ HVDVÃQà WHúNLO HGLSBurgers denkleminin nümerik çözümleri elGH HGLOPLúWLU $/UÃFD NXOODQÃODQ/QWHPOHULQNDUDUOÃOÃNDQDOL]L/DSÃOPÃúWÃU$OWÃQFà EOÂP /LQH tezin temelNÃVPÃROXS/QWHPOHUGHQNOHPHGR÷UXGDQuygulanDUDNQÂPHULNo]ÂPOHUHOGHHGLOPLúWLUYedinci bölümde, elde edilen VRQXoODUÃQNDUúÃODúWÃUÃOPDVÃYHULOPHNWHGLUBurgers denklemi, Method of Lines, Euler yöntemi,$1$+7$5 .(/ø0(/(5mertebeden ve Dördüncü mertebeden Runge-Kutta yöntemleri, Crank-øNLQFLNicolson yöntemi, Matris yöntemi.

ABSTRACTM.Sc. ThesisA SEMI-ANALITIC APPLICATIONFOR SOLUTION OF BURGERS? EQUATIONDerya TÜRKøQQÂ8QLYHUVLW/Graduate School of Natural and Applied SciencesDepartment of Mathematics75 + x pages2005Supervisor : Assoc. Prof. $OLg='(ùThis thesis consists of seven chapters.In chapter 1, it is devoted to Burgers? equation that is used as a modelproblem in this study.In chapter 2, it is briefly introduced general concepts, theorem and methodsconcerning with the subject.In chapter 3, The Method of Lines is explained and applied to a problem.In chapter 4, equation is given.DQDOLWLFVROXWÃRQRI%XUJHUV?Chapter 5 is the main part of this study in which numerical solutions ofBurgers? equation reduced by the Hopf-Cole transformation are obtained. Also,stability of the methods is investigated.Chapter 6 is also important part of this thesis. In this chapter, themethods are directly applied to Burgers? equation.In chapter 7, it is given the comparison of the obtained numerical solutions.KEYWORDS: Burgers? equation, Method of Lines, Euler method, 2. order and 4.order Runge-Kutta methods, Crank-Nicolson method, Matrix method.