Causon, D.M. and Mingham, C.G. (2010) Introductory Finite Difference Methods for PDEs.

has been cited by the following article:

• TITLE: Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation

  AUTHORS: Md. Shahadat Hossain Mojumder, Md. Nazmul Haque, Md. Joni Alam

  KEYWORDS: Explicit Scheme, Implicit Scheme, C-N Scheme, CFL Condition

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.10, October 31, 2023

  ABSTRACT: In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known numerical technique for obtaining the approximate solutions of an initial boundary value problem. We develop Forward Time Centered Space (FTCS) and Crank-Nicolson (CN) finite difference schemes for one-dimensional heat equation using the Taylor series. Later, we use these schemes to solve our governing equation. The stability criterion is discussed, and the stability conditions for both schemes are verified. We exhibit the results and then compare the results between the exact and approximate solutions. Finally, we estimate error between the exact and approximate solutions for a specific numerical problem to present the convergence of the numerical schemes, and demonstrate the resulting error in graphical representation.