Uniformly convergent finite difference operator method for function of single variable

The course project introduces the numerical analysis of different types of equations, describing the mathematical background for understanding numerical methods and giving information on what to expect when using them. As a reason for studying numerical methods as a part of a more general course on different types of equations, many of the basic ideas of the numerical analysis of different types of equations are tied closely to theoretical behaviour associated with the problem being solved. For example, the criteria for the stability of a numerical methods are closely connected to the stability of the different types of problems being solved. We also include MATLAB programs to illustrate many of the ideas that are introduced in the course project. Much is to be learned by experimenting with the numerical solution of different types of equations. Numerical methods vary in their behavior, and the many different types of problems affect the performance of numerical methods in a variety of ways.