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A higher-order method for nonlinear singular two-point boundary value problems
We present a finite difference method for a general class of nonlinear singular two-point boundary value problems. The order of convergence of the method for such a general class of problems is higher than the previous reported methods. The method yields a fourth-order convergence for the special case p(x)=w(x)=xα, α≥1
An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
We present the first stable dynamical numerical evolutions of the Einstein
equations in terms of a conformally rescaled metric on hyperboloidal
hypersurfaces extending to future null infinity. Axisymmetry is imposed in
order to reduce the computational cost. The formulation is based on an earlier
axisymmetric evolution scheme, adapted to time slices of constant mean
curvature. Ideas from a previous study by Moncrief and the author are applied
in order to regularize the formally singular evolution equations at future null
infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime
are obtained, including a gravitational perturbation. The Bondi news function
is evaluated at future null infinity.Comment: 21 pages, 4 figures. Minor additions, updated to agree with journal
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