DSM for general nonlinear equations

作者：Ramm A G^*

来源：Applied Mathematics Letters, 2012, 25(12): 2009-2014.

DOI：10.1016/j.aml.2012.06.006

• Nonlinear operator equations
• Iterative methods
• DSM Dynamical Systems Method

If F:H -%26gt; H is a map in a Hilbert space H, F is an element of C-loc(2), and there exists a solution y, possibly non-unique, such that F(y) = 0, F%26apos;(y) not equal 0, then equation F(u) = 0 can be solved by a DSM (Dynamical Systems Method) and the rate of convergence of the DSM is given provided that a source-type assumption holds. A discrete version of the DSM yields also a convergent iterative method for finding y. This method converges at the rate of a geometric series. Stable approximation to a solution of the

• 出版日期2012-12