# 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} }

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…

## 92 Citations

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## References

SHOWING 1-6 OF 6 REFERENCES

### Über die partiellen Differenzengleichungen der mathematischen Physik

- Mathematics
- 1928

----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung…

### On mildly nonlinear partial difference equations of elliptic type

- Mathematics
- 1953

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

- R. Wasow, Finite difference methods for partial differential equations, Wiley, New York,
- 1960

### Relaxation methods for linear equations, Comm

- Pure Appl. Math,
- 1959