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

TL;DR

This paper introduces a new numerical method based on the Fokas method for efficiently computing Neumann controls for the heat equation, achieving small errors and easy extension to other PDEs.

Contribution

The paper develops a direct, efficient numerical algorithm for Neumann control of the heat equation using the Fokas method, with broad applicability to linear PDEs.

Findings

Requires small computational effort

Achieves exponentially small error

Easily extendable to other PDEs

Abstract

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.