Numerical solutions of the Fisher's equation by using quintic B-spline functions

The Fisher (KKP) equation is an important partial differential equation which arises in the study of many physical systems. In this MSc. Thesis, numerical solutions of the Fisher (KKP) equation based on Collocation methods using Quintic B-spline functions are investigated. The thesis is consist of five parts.In the first chapter of the thesis,approximation methods and summary of the literature is mentioned.In the second chapter, theoretical aspects of polynomial approximation methods is focused on. In the third chapter, Spline functions, B-spline functions and some properties of them are explained. Quadratic, cubic, quartic and quintic functions are given. In the fourth section, the Fishers? equation is introduced together with initial and boundary conditions. Some of the previous numerical methods about the equation are mentioned shortly and numerical solutions of the Fishers? equation are obtained with Collocation methods using quintic B-spline functions.The stability analysis of the numerical technic based on Von Neumann theory is given. In the fifth section, the collocation method which is given to solve the Fishers? equation is tested by using test problems with modified of equation under the different initial conditions.Then numerical solutions of Fisher equation are obtained with collocation methods by using quintic B-spline functions. As a result, Collocation method with B-spline functions give adequately good results. Computed results are compared with the numerical results given by previous authors. So it is recommended that B-spline functions can be used for solving other nonlinear partial differential equations.