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We deene the Newton iteration for solving the equation f y = 0, where f is a map from a Lie group to its corresponding Lie algebra. Two v ersions are presented, which are formulated independently of any metric on the Lie group. Both formulations reduce to the standard method in the Euclidean case, and are related to existing algorithms on certain Riemannian… (More)

Several a posteriori error estimates for the Stokes equations have been derived by several authors. In this paper we compare some estimates based on the solution of local Stokes systems with estimates based on the residuals of the discretized finite element equations. Their performance as local indicators as well as global estimates is investigated.

- Z Jackiewicz, B Owren, B Welfert
- 1998

The performance of the waveform relaxation method for solving systems of ODEs depends largely on the choices that are made for splitting, size of time window, and preconditioning. Although it is known that superlinear convergence is obtained on finite time windows, the convergence may be slow in the first few iterations. We propose the use of pseudcepectra… (More)

- R E Bank, B D Welfert, +5 authors D Silvester
- 1997

In this work we have derived an eecient and eeective adaptive mesh reenement strategy for a stabilised implementation of the lowest order P 1 { P 0 mixed nite element method for steady incompressible Stokes ow. Our analysis indicates that the accuracy of simple a-posteriori error estimators is independent of the stabilisation parameter, and that if the… (More)

We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are… (More)

- M. Rahman, Zdzislaw Jackiewicz, Bruno D. Welfert
- Applied Mathematics and Computation
- 2007

- John W. Jones, Bruno D. Welfert
- Adv. Comput. Math.
- 1995

- Angelamaria Cardone, Zdzislaw Jackiewicz, James H. Verner, Bruno D. Welfert
- J. Computational Applied Mathematics
- 2015

We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to… (More)

- Kyriakos Kitsios, Andreas Spanias, Bruno D. Welfert
- Signal Processing
- 2002

- Marc Nico Spijker, S. Tracogna, Bruno D. Welfert
- Math. Comput.
- 2003

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