Numerical computation of Neumann controllers for the heat equation on a finite interval

This paper presents a new numerical method which approximates Neumann type null controllers for the heat equation and is based on the Fokas method. This is a direct method for solving problems originating from the control theory, which allows the realisation of an efficient numerical algorithm that requires small computational effort for determining the null controller with exponentially small error. Furthermore, the unified character of the Fokas method makes the extension of the numerical algorithm to a wide range of other linear PDEs and different type of boundary conditions straightforward.