188 research outputs found
Approximation by the Legendre collocation method of a model problem in electrophysiology
No full textAbstractWe examine the polynomial approximation of the solution of a nonlinear differential problem modelling the evolution of the potential inside an electrically stimulated neuron. The collocation method at the Legendre Gauss-Lobatto nodes is used for the discretization with respect to the space variable
The Space-Time Metric Outside a Pulsating Charged Sphere
No full textWe consider the problem of determining the dynamics of the electromagnetic field generated outside a ball whose charge changes depending on time. We are in conditions of perfect symmetry and the electric field is considered to be radial. This is not a simplification since, under such a hypothesis, the magnetic field does not develop. Thus, it is first necessary to find out the appropriate modeling equations. These are obtained by writing a suitable energy tensor that combines the classical electromagnetic stress-energy tensor with a special kind of mass tensor. The next step is to show that it is possible to solve Einstein’s equations by plugging the new tensor on the right-hand side. Interesting connections with some classical solutions related to black holes are finally established
Inverse inequalities for chebyshev approximations in L∞ norms
No full textAbstractInverse inequalities in the space of polynomials, relating the maximum norm in [-1,1] and weighted Sobolev norms, are shown
Some results about the spectrum of the chebyshev differencing operator
No full textA spectral method in space and a finite-difference scheme in time are employed to approximate the solution of the model equation: yt=yx. The operator ∂/∂x is discretized by the collocation method based on the Chebyshev nodes. The second order Runge-Kutta method is used for the operator ∂/∂t. It is known that the location, in the complex plane, of the eigenvalues of the collocation matrix is crucial for the stability. A simple way of computing the coefficients of the characteristic polynomial of that matrix is shown. An explicit computation of the roots gives indications on the choice of the time step. © 1987, Elsevier B.V
A fast solver for elliptic boundary-value problems in the square
No full textWe approximate the solution of advection-diffusion equations by collocation at a special grid related to the differential operator and the classical Legendre grid
Convergence analysis for pseudospectral multidomain approximations of linear advection equations
No full textLegendre and Chebyshev collocation schemes are proposed for the numerical approximation of first order linear hyperbolic equations, by a domain decomposition procedure. Spectral convergence estimates are provided both for Legendre and Chebyshev Gauss-Lobatto nodes. © 1989 Oxford University Press
Improving the Performances of Implicit Schemes for Hyperbolic Equations
No full textConsidering that, in the discretization of linear differential operators, one can choose suitable nodes of super-convergence for the evaluation of the residual, we apply this idea to first-order operators associated with the approximation of hyperbolic equations, in order to improve some known implicit schemes
Error estimates for spectral approximation of linear advection equations over an ipercube
No full textSpectral and pseudospectral (collocation) approximations of the advection equations in an ipercube are presented. Collocation is imposed on the Chebyshev nodes. Stability and convergence results are given in Sobolev norms relative to some Jacobi weights. © 1984 Instituto di Elaborazione della Informazione del CNR
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