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A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation
Author(s) -
Johns Peter B.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110810
Subject(s) - simple (philosophy) , mathematics , stability (learning theory) , finite difference , diffusion , transmission line , diffusion equation , finite difference method , computer science , numerical analysis , line (geometry) , exact solutions in general relativity , calculus (dental) , mathematical analysis , physics , geometry , engineering , telecommunications , medicine , philosophy , metric (unit) , operations management , dentistry , epistemology , machine learning , thermodynamics
Abstract This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission‐line modelling (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.