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On a new method for enlarging the radius of convergence for Newton's method

Ioannis K. Argyros (2001)

Applicationes Mathematicae

We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.

On a nonlinear elliptic system: resonance and bifurcation cases

Mario Zuluaga Uribe (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider an elliptic system at resonance and bifurcation type with zero Dirichlet condition. We use a Lyapunov-Schmidt approach and we will give applications to Biharmonic Equations.

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