# ITERATION METHODS FOR NONLINEAR PROBLEMS

```@article{Schechter1962ITERATIONMF,
title={ITERATION METHODS FOR NONLINEAR PROBLEMS},
author={Samuel Schechter},
journal={Transactions of the American Mathematical Society},
year={1962},
volume={104},
pages={179-189}
}```
• S. Schechter
• Published 1962
• Mathematics
• Transactions of the American Mathematical Society
Analogous methods have been used in practice, with apparent success, on nonlinear problems as well. For the most part, these have not been justified mathematically and this work is an attempt to fill this gap. In particular it is shown that the relaxation methods yield solutions to problems arising from the minimization of certain convex functions. In practice, these functions are obtained by approximating multiple integrals in a calculus of variations problem. It is shown that an approximate…
• Computer Science
• 2001
Finite difference and finite element methods are used with nonlinear SOR to solve the problems of minimizing strict convex functionals and boundary grid refinements play an essential role in the proposed non linear SOR algorithm.
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The minimal surface equation is solved numerically by use of the method studied previously by the author for solving the two -dim en-sirinal nonlinear magnetostatic-field equation. The method
We describe in this report the numerical analysis of a particular class of nonlinear Dirichlet problems. We consider an equivalent variational inequality formulation on which the problems of
SummaryOn the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of
this study is a continuation of a previous paper [Computing 38 (1987), pp.117–132]. In this paper, we consider the successive overrelaxation method with projection for obtaining finite element

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----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung
The use of t he fini te differences met hod is in solving t he boundary value problem of t he first kind for t he nonlinear elliptic equation A</> = F (X,y,</>, </>., cf>u) is justified by first

### From (8.3) it follows immediately that au(u)^4p and, by the argument of §5, En is a solvent set. Condition (9.1) also implies that for every i>°£-E,, Ko is bounded

• <¡?) denotes the smallest eigenvalue of <í>

### and W

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