Smooth Representation of Functions on Non-Periodic Domains by Means of the Fourier Continuation Method

The Fourier Continuation (FC) method[1] provides a smooth, periodic continuation to a non-smooth function. This allows for a Fourier series to be used in the solution of Partial Differential Equations where periodicity is not applicable. Furthermore this provides a smooth continuous interpolation of the function throughout the domain. In this investigation the accuracy of the Fourier series and it's derivative was compared to the analytical solution. Introduction