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Improved difference approximations to the heat equation
Author(s) -
Lick Wilbert
Publication year - 1985
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.1620211103
Subject(s) - mathematics , differential equation , partial differential equation , cartesian coordinate system , mathematical analysis , ftcs scheme , finite difference method , heat equation , ordinary differential equation , separable partial differential equation , thermal conduction , independent equation , numerical partial differential equations , differential algebraic equation , physics , geometry , thermodynamics
A method for obtaining difference equations from differential equations which has previously been applied to ordinary differential equations is here applied to the time‐dependent heat conduction equation as a representative example of parabolic partial differential equations. Explicit difference equations are derived which are stable for all values of αΔt/Δ 2 and are also accurate. Implicit‐algorithms with improved accuracy are also derived. Problems in cartesian and cylindrical co‐ordinates are treated.