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Monotonicity of Brown's Method
Author(s) -
Frommer A.
Publication year - 1988
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19880680211
Subject(s) - iterated function , monotonic function , mathematics , sequence (biology) , nonlinear system , boundary value problem , iterative method , order (exchange) , mathematical analysis , mathematical optimization , physics , genetics , finance , quantum mechanics , economics , biology
Sufficient conditions are given in order that the iterates of Brown's method converge monotonically to a solution of a system of (nonlinear) equations. It is shown that in many cases it is possible to construct a second sequence of iterates such that each iteration step yields an inclusion for a solution of the system. Similar results hold for the analytic and the multistage modifications of Brown's method. The monotonicity results apply in particular to discrete analogs of certain ordinary and elliptic boundary value problems and integral equations. A numerical example is included.