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Solving the reaction–diffusion equations with nonlocal boundary conditions based on reproducing kernel space
Author(s) -
Lin Yingzhen,
Zhou Yongfang
Publication year - 2009
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.20409
Subject(s) - mathematics , kernel (algebra) , boundary value problem , space (punctuation) , reaction–diffusion system , mathematical analysis , diffusion , partial differential equation , boundary (topology) , function (biology) , pure mathematics , physics , computer science , evolutionary biology , biology , thermodynamics , operating system
The reaction–diffusion equations with initial condition and nonlocal boundary conditions are discussed in this article. A reproducing kernel space is constructed, in which an arbitrary function satisfies the initial condition and nonlocal boundary conditions of the reaction‐diffusion equations. Based on the reproducing kernel space, a new algorithm for solving the reaction–diffusion equations with initial condition and nonlocal boundary conditions is presented. Some examples are displayed to demonstrate the validity and applicability of the proposed method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009