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A second‐order linearized difference scheme on nonuniform meshes for nonlinear parabolic systems with Dirichlet boundary value conditions
Author(s) -
Zhang LingYun,
Sun ZhiZhong
Publication year - 2003
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.10065
Subject(s) - mathematics , boundary value problem , nonlinear system , mathematical analysis , dirichlet boundary condition , polygon mesh , dirichlet distribution , dirichlet problem , norm (philosophy) , partial differential equation , order (exchange) , scheme (mathematics) , parabolic partial differential equation , geometry , physics , finance , quantum mechanics , political science , law , economics
Abstract A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Dirichlet boundary value problem of the nonlinear parabolic systems. It is proved that the difference scheme is uniquely solvable and second order convergent in L ∞ ‐ norm. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 638–652, 2003