A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation
Abstract
This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission-line modeling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit Crank-Nicolson routine may be expressed as the exact solution of certain transmission-line models. Using these models a technique for comparing the accuracy and stability of numerical routines is developed and a detailed comparison of the new TLM methods and the well established methods is made.
- Publication:
-
International Journal for Numerical Methods in Engineering
- Pub Date:
- 1977
- DOI:
- 10.1002/nme.1620110810
- Bibcode:
- 1977IJNME..11.1307J
- Keywords:
-
- Diffusion Waves;
- Finite Difference Theory;
- Mathematical Models;
- Maxwell Equation;
- Numerical Stability;
- Transmission Lines;
- Analog Simulation;
- Approximation;
- Diffusion Theory;
- Electric Power Transmission;
- Error Analysis;
- Propagation Modes;
- Physics (General)