İkili Burgers denkleminin trigonometrik B-spline kollokasyon yöntemi ile nümerik çözümleri

MEHMET KEREM YİĞİT

İkili Burgers denkleminin trigonometrik B-spline kollokasyon yöntemi ile nümerik çözümleri

Thesis Type: Postgraduate

Institution Of The Thesis: Inonu University, Fen Bilimleri Enstitüsü, Matematik, Turkey

Approval Date: 2021

Thesis Language: Turkish

Student: MEHMET KEREM YİĞİT

Principal Supervisor (For Co-Supervisor Theses): Yusuf Uçar

Co-Supervisor: Nuri Murat Yağmurlu

Open Archive Collection: AVESIS Open Access Collection

Abstract:

This master thesis consists of five chapters. In the first chapter, the main purpose of the thesis was briefly mentioned and some information about the finite element method was given. In the second chapter, information was given about the basic concepts that we used in this thesis, the finite element method, the collocation method and trigonometric B-spline basis functions. In addition, in this chapter, the historical development of the finite element method, which is going to be considered in the thesis, is mentioned. In the third chapter, the studies related to the coupled Burgers equation in the literature are presented and three model problems of the coupled Burgers equation to be solved numerically with different boundary and initial conditions are introduced. In the fourth chapter, using two different linearization techniques, LIN-1 and LIN-2, instead of the non-linear terms in the coupled Burgers equation, numerical schemes were obtained by cubic and quintic trigonometric B-spline collocation finite element method. The numerical results obtained by applying these schemes to the three models given in the previous section were compared with the available exact solution and/or the results from different studies in the literature in tabular form. Since the stability analysis of the numerical schemes obtained in both linearization techniques are going to be similar, the stability analysis of the schemes obtained by the cubic trigonometric B-spline collocation methods for LIN-1 and LIN-2 was examined by the von Neumann method. In the fifth and last part, the results obtained from both applied linearization techniques were compared for each model problem in the form of tables.