Numerical Computation of Neumann Controls for the Heat Equation on a Finite Interval

This article presents a new numerical method, which approximates Neumann type null controls 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 realization of an efficient numerical algorithm that requires small computational effort for determining the null control 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 partial differential equations and different type of boundary conditions straightforward.