This paper 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 realisation 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 PDEs and different type of boundary conditions straightforward.

翻译：本文件介绍了一种新的数字方法,它近似于Neumann型热方程式的无效控制,并以Fokas法为基础。这是一种直接解决控制理论引起的问题的方法,可以实现一个高效的数字算法,它需要小的计算努力,才能用指数小的错误来确定无效控制。此外,Fokas方法的统一性使得数字算法扩展到其他线性PDE和不同类型的边界条件的范围很广。