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Convergence of the lines method for first‐order partial differential‐functional equations
Author(s) -
ZubikKowal Barbara
Publication year - 1994
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.1690100310
Subject(s) - mathematics , convergence (economics) , nonlinear system , mathematical analysis , boundary value problem , method of lines , argument (complex analysis) , partial differential equation , differential equation , first order partial differential equation , class (philosophy) , ordinary differential equation , differential algebraic equation , biochemistry , chemistry , physics , quantum mechanics , economics , economic growth , artificial intelligence , computer science
Initial‐boundary value problems for nonlinear differential‐functional equations are considered. A general class of lines method is investigated. The Perron‐type estimation for the right‐hand side of the equation with respect to the functional argument is assumed. The proof of the convergence is based on a comparison theorem for differential‐difference inequalities. A numerical example is given. © 1994 John Wiley & Sons, Inc.