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Fully discrete arbitrary‐order schemes for a model parabolic equation
Author(s) -
Shi J.
Publication year - 1994
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650191106
Subject(s) - mathematics , advection , scalar (mathematics) , numerical diffusion , parabolic partial differential equation , convection–diffusion equation , numerical stability , mathematical analysis , stability (learning theory) , numerical analysis , order of accuracy , ftcs scheme , order (exchange) , partial differential equation , differential equation , geometry , physics , mechanics , computer science , ordinary differential equation , machine learning , thermodynamics , differential algebraic equation , finance , economics
A fully discrete methodology is investigated from which two‐level, explicit, arbitrary‐order, conservative numerical schemes for a model parabolic equation can be derived. To illustrate this, fully discrete three‐, five‐, seven‐ and nine‐point conservative numerical schemes are presented, revealing that a higher‐order scheme has a better stability condition. A method from which high‐order numerical schemes for a scalar advection‐diffusion equation can be developed is discussed. This method is based on high‐order schemes of both the advection and diffusion equations.