Discrete Maximum Principle in One-Dimensional Heat Equation - K.C., Durga Jang; Basnet, Ganesh Bahadur (Journal of Advanced College of Engineering and Management, 2016)
The maximum principle plays key role in the theory and application of a wide class of real linear partial differential equations. In this paper, we introduce ‘Maximum principle and its discrete version’ for the study of second-order parabolic equations, especially for the one-dimensional heat equation. We also give a short introduction of formation of grid as well as finite difference schemes and a short prove of the ‘Discrete Maximum principle’ by using different schemes of heat equation. Journal of Advanced College of Engineering and Management, Vol. 2, 2016, Page: 5-10