A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper, a compact difference scheme is established for the heat equations with multi-point boundary value conditions. The truncation error of the difference scheme is O(τ2+h4),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\tau ^2+h^4),$$\end{document} where τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document} and h are the temporal step size and the spatial step size. A prior estimate of the difference solution in a weighted norm is obtained. The unique solvability, stability and convergence of the difference scheme are proved by the energy method. The theoretical statements for the solution of the difference scheme are supported by numerical examples.