Özet:
This doctoral dissertation consists of eight chapters, focusing on the Önding the
numerical solutions of RLW, Burgersí, AD and Fisher equations by using the least
squares exponential B-spline method.
In the introduction chapter, scope and purpose of the dissertation was explained
such as the questions why numerical solutions are developed and spline functions are
preferred answered, despite the fact that di§erential equations have analytical solutions
under various initial and boundary conditions.
In the second chapter of the dissertation, literature review of the equations to be
solved and the methods to be used for such was given. Next, information regarding
soliton and solitary waves and the usage areas of these waves was given. After that,
weighted residuals method, spline functions and exponential B-spline functions were
deÖned. In the last part of this chapter RLW, Burgersí, AD and Fisher equations were
deÖned.
Respectively in the following chapters, numerical solutions of RLW, Burgersí, AD
and Fisher equations were obtained by using least squares exponential B-spline method
and the reliability of the solutions were checked by using testing problems. In addition,
acquired numerical solution data was interpreted via tables and Ögures.
In the last two parts of the doctoral dissertation, the data obtained in the study
were summarized and discussed, and suggestions were made for the next researches
