Multi-step exponential B-spline collocation method for solving EW equation

This master's thesis consists of seven chapters, focusing on the solution of the EW equation using the Multistep Exponential B-Spline Collocation method. In the first chapter, we delve into mathematical modeling of problems encountered in various scientific fields. We explore solution methods alongside differential equations when analytical solutions are not feasible. Additionally, we discuss why spline functions are preferred in such cases, providing an overview of the thesis scope and objectives. The second chapter reviews previous work related to solving the equations at hand. The third chapter introduces fundamental concepts and terminology. We explain solitons, solitary waves, and their applications. Subsequently, we delve into spline functions, B-spline functions, and exponential B-spline functions. Towards the end of this chapter, we define the EW equation and examine it in detail. In the fourth and fifth chapters, we employ the three-step and four-step Exponential BSpline Collocation methods to numerically solve the EW equation. We validate the reliability of our solutions using test problems. The obtained numerical results are evaluated through tables and figures. Key Words: Exponential B-spline, Collocation method, EW equation, Multi-step methods