About the solutions by the B-spline method of differential equations

A short introduction about the Finite Difference and Collocation Methods are given in the first chapter. By giving definition and properties of spline functions, cubic spline and B-spline interpolation are formed.In the second chapter, one-dimensional linear heat equation is solved by using cubic B-spline Collocation Method. The method is tested for the initial and boundary conditions of heat equation.In the third chapter, the solution of the equation with lateral heat loss given initial and boundary conditions is expressed by using the cubic B-spline functions as approximation functions in the method.In the second and third chapters, the data which is get to numerical solution are shown in the table and stability of the method is investigated by Fourier stability analysis. Finally, Fortran Programme which used to the numerical analysis is given.