Application of finite difference method of lines on the heat equation

• Published in: Numerical methods for partial differential equations Vol. 34; no. 2; pp. 626 - 660
• Main Authors: Kazem, Saeed, Dehghan, Mehdi
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc 01.03.2018
• Subjects: Differential equations; Dirichlet problem; Eigenvalues; Eigenvectors; exponential matrix; Finite difference method; heat equation; implicit and explicit methods; Method of lines; Thermodynamics; tridiagonal matrix

In this article, we apply the method of lines (MOL) for solving the heat equation. The use of MOL yields a system of first–order differential equations with initial value. The solution of this system could be obtained in the form of exponential matrix function. Two approaches could be applied on thi...