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Computational considerations in non‐linear diffusion
Author(s) -
Mingle John O.
Publication year - 1973
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.1620070202
Subject(s) - linear system , boundary value problem , mathematics , numerical analysis , quadrature (astronomy) , computer science , computation , redundancy (engineering) , finite element method , method of fundamental solutions , mathematical optimization , algorithm , mathematical analysis , boundary element method , singular boundary method , physics , operating system , optics , thermodynamics
The numerical solution of non‐linear diffusion problems is considered from the computational view‐ point. The advantage of various aspects of the problem solution are considered toward enhancing the computational understanding of the system. First is the analytical solution to the reduced linear case which acts as an error check on the numerical solutions as well as providing a base for a perturbation theory approach. Next are two different numerical solutions which are utilized to generate solution redundancy. These are based upon the method of differential quadrature and the method of finite differences. The application to non‐linear transient slab diffusion with a general reservoir boundary condition is shown as an example of the various methods.