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We de ne 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 versions 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)

- K . J . in ’ t Hout, Bruno D. Welfert
- 2006

We consider Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection–diffusion equations with cross derivative terms. We derive new linear stability results for three ADI schemes that have previously been studied in the literature. These results are subsequently used to show that the ADI… (More)

When numerically solving a set of partial differential equations through a finite element strategy associated with a weak formulation, one usually faces the problem of increasing the accuracy of the solution without adding unnecessary degrees of freedom in non-critical parts of the computational domain. In order to identify these regions, indicators were… (More)

- R E Bank, Bruno D. Welfert, +5 authors David J. 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)

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

This paper extends the results of synaptically generated wave propagation through a network of connected excitatory neurons to a continuous model, defined by a Fredholm Volterra integro-differential equation (FVIDE), which includes memory effects of the past in the propagation. Stochastic approximation and numerical simulations are discussed. 2006 Elsevier… (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)

- Zdzislaw Jackiewicz, Bruno D. Welfert
- J. Sci. Comput.
- 2003

We first extend the stability analysis of pseudospectral approximations of the one-dimensional one-way wave equation “u “x=c(x) “u “x given in [11] to general Gauss–Radau collocation methods. We give asufficient condition on the collocation points for stability whichshows that classical Gauss–Radau ultraspherical methods are perfectly stable while their… (More)

- Bruno D. Welfert
- J. Comput. Physics
- 2007

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

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