Finite difference solutions of the one-dimensional Burgers-like equations

ABSTRACTMSc. ThesisFINITE DIFFERENCE SOLUTIONS OF THEONE-DIMENSIONAL BURGERS-LIKE EQUATIONSYUSUF UÇARİnönü UniversityGraduate School of Natural and Applied SciencesDepartment of Mathematics178 + xxi pages2005Supervisor : Assoc. Prof. Selçuk KUTLUAYThis MSc. thesis consists of five chapters. In the first chapter, basicconcepts of finite difference methods and stability analysis were given.In the second chapter, previous studies on one-dimensional Burgersequation were mentioned. Also in this chapter Hopf-Cole transformation andmodel problems for Burgers equation to be considered in this study were given.In the third chapter, some finite difference methods were applied tothe Burgers equation after the linearization by Hopf-Cole transformation. Thestability analysis of the methods used in this chapter was also investigated.In the fourth chapter, the nonlinear term U Ux in the Burgers equationwas replaced by various finite difference approximations to obtain numericalisolutions. The obtained numerical results were compared with analytical re-sults and those given by previous authors.In the fifth chapter, the numerical results obtained in third and fourthchapters were evaluated. The computed results were found to be in good agree-ment with analytical solution of each problem and published numerical results.KEYWORDS: Burgers Equation, Finite Difference Methods, Hopf-ColeTransformation.ii