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A family of numerical methods for diffusion and reaction–diffusion equations
Author(s) -
Twizell E. H.,
Khaliq A. Q. M.
Publication year - 1986
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690020104
Subject(s) - mathematics , reaction–diffusion system , diffusion , dimension (graph theory) , partial differential equation , order (exchange) , mathematical analysis , parabolic partial differential equation , space (punctuation) , pure mathematics , computer science , thermodynamics , physics , finance , economics , operating system
A family of methods is developed for the numerical solution of second‐order parabolic partial differential equations in one space dimension. The methods are second‐, third‐, or fourth‐order accurate in time; five of them are seen to be L 0 ‐stable in the sense of Gourlay and Morris, while the sixth is seen to be A 0 ‐stable, The methods are tested on four problems from the literature, three diffusion problems and one reaction–diffusion problem.