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A pseudo-spectral method with an absorbing outer boundary is used to solve a set of timedependent force-free equations. In this method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergence-free state of the magnetic field is enforced analytically by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be reproduced well by our pseudo-spectral code. Further, the method is used to present a time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well and the spin-down luminosity obtained in the steady state is in good agreement with the value given by Spitkovsky. [ABSTRACT FROM AUTHOR]

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