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We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the norm. We prove optimal order a priori error estimates in the and norms, under mild mesh conditions for two and three space dimensions.
We discretize the nonlinear Schrödinger equation,
with Dirichlet boundary conditions, by a linearly
implicit two-step finite element method which conserves
the L2 norm. We prove optimal order a priori error
estimates in the L2 and H1 norms, under
mild mesh conditions for two and three space dimensions.
Currently displaying 561 –
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