Two-step methods with one off-step node

One step forward

Two-step Newton methods

We present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach under the same computational cost over other studies such as [9–25] for the semilocal convergence case are: weaker sufficient convergence conditions, more precise error bounds on the distances...

Block Implicit One - Step Methods

A class of one-step methods which obtain a block of r new values at each step are studied. The asymptotic behavior of both implicit and predictor-corrector procedures is examined.

One-step two-wavelength holography.

One-step two-wavelength holography is obtained with twointerferometric beams with different wavelengths by means of apolarizing modulation produced by a liquid-crystal lightvalve. This holographic method eliminates the need for preliminarystatic recording of the hologram and permits one-step two-wavelengthholographic testing to produce results easily in real time.

Two-step W-methods with Parallel Stages

Two-step W-methods are linearly implicit time-stepping methods using s external stages that may be processed in parallel. Methods with order s + 1 and stage order s exist. Appropriate generalizations for the concepts of A-and L-stability are derived as well as necessary conditions for A-stability and suucient conditions for stii accuracy. We construct methods of order four where no order reduct...