Shannon-Taylor technique for solving one-dimensional inverse heat conduction problem

The Shannon-Taylor interpolation technique was introduced by Butzer and Engels in 1983. In this work, the sinc-function is replaced by a Taylor approximation polynomial. In this work, we implement the Shannon-Taylor approximations to solve a one-dimensional heat conduction problem. One of the major advantages of this approach is that the resulting linear system of equations of the approximation procedure has an explicit coefficient matrix. This is not the case of the classical sinc methods due to finite integrals involving e-x2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{-x^2}$$\end{document}. We establish rigorous error estimates involving an additional Taylor’s series tail. Numerical illustrations are depicted.