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A second‐order linearized difference scheme on nonuniform meshes for nonlinear parabolic systems with Neumann boundary value conditions
Author(s) -
Zhang Lingyun,
Sun Zhizhong
Publication year - 2004
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.10088
Subject(s) - mathematics , nonlinear system , boundary value problem , polygon mesh , neumann boundary condition , mathematical analysis , norm (philosophy) , von neumann stability analysis , partial differential equation , scheme (mathematics) , geometry , physics , quantum mechanics , political science , law
A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Neumann boundary value problem of a nonlinear parabolic system. It is proved that the difference scheme is uniquely solvable and second‐order convergent in L ∞ ‐norm. A numerical example is given. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 230–247, 2004