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An ETD Crank‐Nicolson method for reaction‐diffusion systems
Author(s) -
Kleefeld B.,
Khaliq A.Q.M.,
Wade B.A.
Publication year - 2012
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.20682
Subject(s) - crank–nicolson method , mathematics , convergence (economics) , reaction–diffusion system , exponential function , partial differential equation , rate of convergence , order (exchange) , variety (cybernetics) , stability (learning theory) , scheme (mathematics) , mathematical analysis , computer science , key (lock) , computer security , statistics , finance , machine learning , economics , economic growth
Abstract A novel Exponential Time Differencing Crank‐Nicolson method is developed which is stable, second‐order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case, we employ a positivity‐preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a wide variety of examples, including chemotaxis and exotic options with transaction cost. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012