Dynamical systems method (DSM) for general nonlinear equations

Details Dynamical systems method (DSM) for general nonlinear equations Dynamical systems method (DSM) for general nonlinear equations

2006-03-10

arxiv.org/abs/math/0603236v1

Mathematics

Numerical Analysis

Scientific paper

If $F:H\to H$ is a map in a Hilbert space $H$, $F\in C^2_{loc}$, and there exists $y$, such that $F(y)=0$, $F'(y)\not= 0$, then equation $F(u)=0$ can be solved by a DSM (dynamical systems method). This method yields also a convergent iterative method for finding $y$, and converges at the rate of a geometric series. It is not assumed that $y$ is the only solution to $F(u)=0$. Stable approximation to a solution of the equation $F(u)=f$ is constructed by a DSM when $f$ is unknown but $f_\d$ is known, where $||f_\d-f||\leq \d$.

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