Numerical solutions of the some equations using nonpolynomial spline functions

This thesis consists of five chapters. In the first chapter, basic concept and equations that used in the thesis are given. In addition, error norms are defined in this section. This error norms are used computed the errors. Literature on the equations has been investigated and the previous studies on the equations have been mentioned. In he second chapter we examined, the solution of the parabolic equation with nonpolynomial spline function. Construction of the solution algorithm, truncation error and stability analysis has been expressed in detail. Computed results are tabulated in table. After that, numerical solution of the Bratu's problem examined and computed results are compared with the Laplace, Decomposition and B-Spline Solution and this situation given in the table. In the fourth chapter well known in literature and frequently used numerical solution of the Burger equation, in the fifth chapter numerical solution of RLW equation examined. Especially to see the effectiveness of the method for RLW equation, solitary wave motion examined. Keywords: Burger Equation, Bratu Problem, Non – Polynomial Spline Functions, Parabolic Equations.