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A new numerical formulation for parabolic differential equations under the consideration of large time steps
Author(s) -
Lee ShongLeih
Publication year - 1988
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.1620260706
Subject(s) - transient (computer programming) , mathematics , parabolic partial differential equation , thermal conduction , boundary value problem , mathematical analysis , differential equation , heat equation , physics , computer science , thermodynamics , operating system
A new numerical formulation is proposed in this investigation for the solution of parabolic differential equations. The time step parameter λ = 2Δτ/(Δχ) 2 under consideration is as large as 2000 such that only a few time steps are needed for the entire regime of transient heat conduction. Along with the formulation, a time scaling transformation is introduced to produce an accurate result for the beginning of a transient process. Although the present formulation makes reference only to the transient heat conduction problem, the idea is equally applicable to parabolic differential equations for other physical phenomena such as transformed boundary layer flow equations.