1,721,004 research outputs found
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
A multidomain spectral approximation of elliptic equations
No full textA spectral approximation for the Poisson equation defined on Ω = ]−1, 1[×] −1,1[ is studied. The domain Ω is decomposed into two rectangular regions and the equation is collocated at the Legendre nodes in each domain. On the common boundary of the two subdomains, suitable conditions are imposed in order to obtain a unique solution from the resulting linear system. Different values of the discretization parameters are allowed in each rectangle. We prove the stability of the scheme and give convergence estimates. The rate of convergence in a single subdomain, depends only on the regularity of the exact solution therein. An efficient preconditioning matrix is proposed
Pseudospectral approximation of a PDE defined on a triangle
No full textA scheme for the approximation by collocation method of an elliptic equation defined on a triangle is proposed. Different solution techniques are examined
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
Electromagnetic fields simulating a rotating sphere and its exterior with implications to the modeling of the heliosphere
Full text linkVector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a ball. The fields satisfy the set of Maxwell's equations, and some connections with magnetohydrodynamics can also be established. The solutions are extended with continuity outside the ball. In order to avoid peripheral velocities of arbitrary magnitude, as it may happen for a rigid rotating body, they are organized to form successive encapsulated shells, with substructures recalling ball-bearing assemblies. A recipe for the construction of these solutions is provided by playing with the eigenfunctions of the vector Laplace operator. Some applications relative to astronomy are finally discussed
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
- …
